How to Multiply Fractions in 3 Easy Steps

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How to Multiply Fractions in 3 Easy Steps

How to Multiply Fractions in 3 Easy Steps

Math Skills: Learn how to multiply fractions by fractions, how to multiply fractions with whole numbers, and how to multiply mixed fractions.

 

Free Step-by-Step Guide: How to Multiply Fractions Explained

 

Once you have learned how to add fractions and how to subtract fractions, you are ready to start multiplying fractions in a variety of scenarios.

This free guide will teach you everything you need to know about how to multiply fractions in the following ways:

The task of having to multiply fractions together may seem challenging at first, but the procedure is actually quite simple and something that you can learn by working through a handful of practice problems, which is exactly what we will be doing in this free step-by-step guide.

While we highly recommend that you work through the guide from start to finish, you can use the quick-links above to jump to a particular topic section.

For all of the problems in this guide, we will be using an easy 3-step strategy that can be used to solve any problem where you have to multiply fractions to get a solution. So, if you can learn how to follow three easy steps, you can correctly answer any multiplying fractions problem!

Are you ready to get started?

Before we start working on the multiplying fractions practice problems, let’s do a quick recap of some key vocabulary terms related to fractions.

How to Multiply Fractions: Vocabulary Recap

This guide uses several math vocabulary terms related to fractions that you will need to be familiar with in order to learn this new math skill. Be sure that you understand the meaning of the following key vocabulary terms before moving forward in this guide.

The Numerator of a Fraction

For any fraction, the numerator is the number at the top of the fraction. For example, the fraction 4/5 has a numerator of 4 since 4 is at the top of the fraction.

The Denominator of a Fraction

For any fraction, the denominator is the number at the bottom of the fraction. For example, the fraction 4/5 has a denominator of 5 since 5 is at the bottom of the fraction.

In this guide, any mention of a numerator is referring to the top number of a fraction and any mention of a denominator is referring to bottom number of a fraction. This relationship between the numerator and the denominator of a fraction is illustrated in Figure 01-A below.

 

Figure 01-A: In any fraction, the numerator is the top number and the denominator is the bottom number.

 

Moving on, let’s recap three more key vocabulary terms and concepts related to fractions:

Whole Numbers

A whole number refers to any number that does not contain any fractions or decimals (i.e. an integer). Some examples of whole numbers include 4, 51, and 263.

Note that any whole number can be expressed in fraction form by rewriting it as a fraction with a denominator of 1. For example, the number 4 can be rewritten as a fraction as 4/1. This fact will come in handy later on when you learn how to multiply a fraction by a whole number.

 

Figure 01-B: How to Rewrite a Whole Number as a Fraction: Rewrite the given whole number as a fraction with a denominator of 1.

 

Proper Fractions

A fraction is a number that represents a part of a whole number. 1/4, 3/5, and 7/8 are all examples of fractions.

Note that proper fractions have a numerator that is smaller than the denominator.

Mixed Fractions (Mixed Numbers)

A mixed fraction (or a mixed number) is any number that represents the sum of a whole number and a proper fraction. For example, 7 5/8 is a mixed number that is equal to the sum of 7 and 5/8.

Note that mixed fractions can also be expressed as improper fractions (fractions whose numerator is greater than its denominator).

 

Figure 02: What is the difference between a whole number, a fraction, and a mixed number.

 

Now that you are familiar with these vocabulary terms, you’re ready to learn how to multiply fractions using our easy 3-step strategy.


How to Multiply Fractions by Fractions

How to Multiply Fractions by Fractions: Example #1

Example #1: 1/2 x 3/4

To solve this first example, where we are tasked with finding the product of 1/2 (one-half) and 3/4 (three-quarters), we will use the following three-step strategy for multiplying fractions:

How to Multiply Fractions in 3 Easy Steps

  • Step One: Multiply the numerators together.

  • Step Two: Multiply the denominators together.

  • Step Three: See if the resulting fraction can be simplified or reduced.

When it comes to multiplying fractions, the process is extremely straightforward, and you can use these three steps to solve any fraction multiplication problem!

So, let’s go ahead and use these three steps to solve this first problem: 1/2 x 3/4 = ?

Step One: Multiply the numerators together.

For this problem, we have two fractions: 1/2 x 3/4

The first step requires us to multiply the two numerators (top numbers) together as follows:

  • 1 x 3 = 3

Step Two: Multiply the denominators together.

The second step requires us to multiply the two denominators (bottom numbers) together as follows:

  • 2 x 4 = 8

Step Three: See if the resulting fraction can be simplified or reduced.

Now we have a new fraction with a numerator of 3 and a denominator of 8:

  • 1/2 x 3/4 = 3/8

For the final step, we have to see if the result can be further simplified or reduced. If it can’t, our result will be our final answer.

In this case, 3/8 can not be simplified or reduced any further and we can conclude that:

Final Answer: 1/2 x 3/4 = 3/8

Figure 03 below illustrates how we solved the first example using the three-step strategy.

 

Figure 03: How to Multiply Fractions: Multiply the numerators together, then multiply the denominators together. Finally, simplify the resulting fraction if possible and you’re done!

 

Note that it’s okay if you are still a little confused. The more experience you gain using this 3-step strategy to multiply fractions, the easier these type of problems will become. Let’s go ahead and work through another example.


How to Multiply Fractions by Fractions: Example #2

Example #2: 5/6 x 4/7

Let’s go ahead and solve Example #2 exactly the same as we did the previous example.

Step One: Multiply the numerators together.

For step one, we have to find the product of the two numerators, 5 and 4:

  • 5 x 4 = 20

Step Two: Multiply the denominators together.

For step two, we have to find the product of the two denominators, 6 and 7:

  • 6 x 7 = 42

Step Three: See if the resulting fraction can be simplified or reduced.

Our result is a fraction with a numerator of 20 and a denominator of 42:

  • 5/6 x 4/7 = 20/42

Can the result, 20/42, be reduced? The answer is yes, because both numbers have a greatest common factor of 2. So, after dividing both the numerator and the denominator by 2, we can conclude that:

Final Answer: 5/6 x 4/7 = 20/42 = 10/21

Figure 04 below illustrates how we determined that 5/6 x 4/7 = 10/21

 

Figure 04: How to Multiply Fractions: Be sure to express your answer in reduced form.

 

Next, let’s go ahead and solve one more practice problem where we’ll have to multiply one fraction by another fraction.


How to Multiply Fractions by Fractions: Example #3

Example #3: 9/16 x 7/12

Again, we can use the same three-step strategy to solve this third example as follows:

Step One: Multiply the numerators together.

In this case, the numerator of the first fraction is 9 and the numerator of the second fraction is 7.

  • 9 x 7 = 63

Step Two: Multiply the denominators together.

In this case, the denominator of the first fraction is 16 and the denominator of the second fraction is 12.

  • 16 x 12 = 192

Step Three: See if the resulting fraction can be simplified or reduced.

Now we have a new fraction with a numerator of 62 and a denominator of 192:

  • 9/16 x 7/12 = 63/192

To see if this result can be reduced, we have to see if 63 and 192 both share a GCF. Since both of these numbers are divisible by 3, we can divide both the numerator and the denominator by 3 to get our final answer in reduced form:

Final Answer: 9/16 x 7/12 = 63/192 = 21/64

The graphic in Figure 05 below shows we successfully multiplied two fractions in this example.

 

Figure 05: How to Multiply Fractions Step-by-Step.

 

Now that you have some experience with multiplying fractions, let’s move onto the next section where you will learn how to multiply a fraction by a whole number and how to multiple a whole number by a fraction.


How to Multiply Fractions with Whole Numbers

The second section of this guide will focus on how to multiply a fraction with by a whole number and how to multiply a whole number by a fraction.

Luckily, the three-step method that we used to solve problems in the previous section will work here as well. If you are unfamiliar with how to multiply a fraction by a fraction, we highly recommend that you go back and work through the above examples.

Now, let’s jump into our first example on how to multiply fractions with whole numbers!

How to Multiply a Fraction by a Whole Number: Example #1

Example #1: 3/8 x 2

When learning how to multiply fractions with whole numbers, it is important to remember that any whole number can be rewritten as an equivalent fraction by rewriting it as a fraction with a denominator of 1.

Since any whole number can be expressed as a fraction in this way, we can solve problems where you have to multiply a fraction by a whole number simply by rewriting the whole number as a fraction and then using the same 3-step strategy from the previous section to solve it.

For this example, we can rewrite the whole number, 2, as 2/1 and rewrite the original problem as:

  • 3/8 x 2 → 3/8 x 2/1

Now, we can find the product by using our three steps:

Step One: Multiply the numerators together.

In this case, the numerator of the first fraction is 3 and the numerator of the second fraction is 2.

  • 3 x 2 = 6

Step Two: Multiply the denominators together.

In this case, the denominator of the first fraction is 8 and the denominator of the second fraction is 1.

  • 8 x 1 = 8

Step Three: See if the resulting fraction can be simplified or reduced.

Finally, we are left with a new fraction with a numerator of 6 and a denominator of 8:

  • 3/8 x 2/1 = 6/8

And, since 6 and 8 are both divisible by 2, we know that the fraction 6/8 can be simplified to:

Final Answer: 3/8 x 2/1 = 6/8 = 3/4

Figure 06 illustrates how we solved this problem.

 

Figure 06: How to Multiply a Fraction by a Whole Number: Rewrite the whole number as a fraction with a denominator of 1.

 

Next, let’s take a look at another example of how to multiply fractions by whole numbers.


How to Multiply a Fraction by a Whole Number: Example #2

Example #2: 5/8 x 6

For this next practice problem, we can rewrite the whole number, 6, as 6/1 and rewrite the original problem as:

  • 5/8 x 6 → 5/8 x 6/1

From here, we can solve this problem as follows:

Step One: Multiply the numerators together.

Start by multiplying the numerators of both fractions together:

  • 5 x 6 = 30

Step Two: Multiply the denominators together.

Next, continue with multiplying the denominators of both fractions together:

  • 8 x 1 = 8

Step Three: See if the resulting fraction can be simplified or reduced.

Here we have a resulting fraction with a numerator of 30 and a denominator of 8:

  • 5/8 x 6/1 = 30/8

Notice that this result is an improper fraction since the numerator, 30, is greater than the denominator, 8. We can reduce this result down to 15/4 and leave it as our final answer or we can convert 15/4 to a mixed number, 3 3/4.

Final Answer: 5/8 x 6/1 = 30/8 = 15/4 or 3 3/4

The graphic in Figure 07 shows how we solved solve this problem by multiplying fractions by whole numbers.

 

Figure 07: How to Multiply a Fraction by a Whole Number Step-by-Step.

 

How to Multiply a Whole Number by a Fraction: Example #3

Example #3: 9 x 2/3

Notice that this third example requires you to multiply a whole number by a fraction (rather than a fraction by whole number like in the last two examples). Since multiplication is associative, the order of the terms won’t change the way that you solve the problem, so we can again use our three-step strategy as follows:

First, just like the previous two examples, rewrite the whole number (9 in this case) as a fraction with a denominator of 1.

  • 9 x 2/3 → 9/1 x 2/3

Step One: Multiply the numerators together.

Multiply the numerators together as follows:

  • 9 x 2 = 18

Step Two: Multiply the denominators together.

Multiply the denominators together as follows:

  • 1 x 3 = 3

Step Three: See if the resulting fraction can be simplified or reduced.

The resulting fraction has a numerator of 18 and a denominator of 3:

  • 9/1 x 2/3 = 18/3

The resulting improper fraction, 18/3, can be simplified. Since both 18 and 3 share a GCF of 3, we can perform 18/3 = 6/1 = 6 and conclude that

Final Answer: 9/1 x 2/3 = 18/3 = 6

All of the steps for solving this example are shown in Figure 08 below.

 

Figure 08 How to Multiply a Whole Number by a Fraction Step-by-Step

 

How to Multiply a Whole Number by a Fraction: Example #4

Example #4: 12 x 7/8

For this next example, we have to rewrite the whole number (12 in this case) as a fraction with a denominator of 1 and then use our three-step strategy to solve:

  • 12 x 7/8 → 12/1 x 7/8

Step One: Multiply the numerators together.

For step one, multiply both of the numerators:

  • 12 x 7 = 84

Step Two: Multiply the denominators together.

For step two, multiply both of the denominators:

  • 1 x 8 = 8

Step Three: See if the resulting fraction can be simplified or reduced.

The result is a new fraction with a numerator of 84 and a denominator of 8:

  • 12/1 x 7/8 = 84/8

Now we have to see if 84/8 can be simplified. Both 84 and 8 share a GCF of 4, so after dividing both numbers by 4, the result is 21/2. While 21/2 can not be simplified further, it is an improper fraction that can be expressed as a mixed number, 10 1/2.

Final Answer: 12/1 x 7/8 = 84/8 = 21/2 or 10 1/2

Figure 09 below illustrates how we were able to multiply a whole number by a fraction to solve this problem.

 

Figure 12: Whenever you end up with an improper fraction, you will likely have to convert it to a mixed number.

 

Now that you know how to multiply a fraction by a whole number and how to multiply a whole number by a fraction, it’s time to move onto the final section where we will go over how to multiply mixed fractions.


How to Multiply Mixed Fractions

How to Multiply Fractions with Mixed Numbers: Example #1

Example #1: 3/5 x 4 1/2

Multiplying fractions with mixed numbers can be done using our same three-step strategy, but with one small extra step at the very beginning.

Before you can solve this problem, you will have to convert the mixed number into an improper fraction.

For this example, the mixed number 4 1/2 can be rewritten as 9/2 (both of these are equivalent):

  • 3/5 x 4 1/2 → 3/5 x 9/2

Now, we can solve 3/5 x 9/2 to find the answer to this problem as follows:

Step One: Multiply the numerators together.

Start off multiplying the numerators of both fractions:

  • 3 x 9 = 27

Step Two: Multiply the denominators together.

Continue by multiplying the denominators of both fractions:

  • 5 x 2 = 10

Step Three: See if the resulting fraction can be simplified or reduced.

After steps one and two, we are left with the improper fraction 27/10.

  • 3/5 x 9/2 = 27/10

While 27/10 can not be simplified, it can be expressed as the mixed number 2 7/10.

Final Answer: 3/5 x 9/2 = 27/10 = 2 7/10

Note that 27/10 is technically a correct answer, but most problems requiring you to multiply mixed fractions will call for you to express your final answer as a mixed fraction.

See Figure 10 for step-by-step details of how we solved this problem.

 

Figure 10: How to Multiply Fractions with Mixed Numbers

 

Moving on, let’s work through one final practice problem where we will have to multiply a mixed number by another mixed number.


How to Multiply Mixed Fractions: Example #2

Example #2: 4 1/5 x 3 2/3

For this example, notice that there are two mixed numbers.

Similar to the previous example, you will have to convert both mixed numbers into equivalent improper fractions before you can use the three-step strategy to solve:

  • 4 1/5 = 21/5

  • 3 2/3 = 11/3

Now we can go ahead and find the answer by solving 21/5 x 11/3

Step One: Multiply the numerators together.

First, find the product of the numerators of both fractions:

  • 21 x 11 = 231

Step Two: Multiply the denominators together.

Next, find the product of the denominators of both fractions:

  • 5 x 3 = 15

Step Three: See if the resulting fraction can be simplified or reduced.

Finally, we are left with the improper fraction 231/15

  • 21/5 x 11/3 = 231/15

While 231/15 is a pretty ugly improper fraction, it can actually be simplified since 231 and 15 share a GCF of 3. So, after dividing both numbers by 3, we are left with 77/5.

  • 21/5 x 11/3 = 231/15 = 77/5

Assuming that we have to express our final answer as a mixed number, we lastly have to rewrite 77/5 as 15 2/5 and we have solved the problem!

Final Answer: 21/5 x 11/3 = 231/15 = 77/5 = 15 2/5

The graphic in Figure 11 below illustrates how we used the 3-step method to solve this problem.

 

Figure 14: How to Multiply Fractions with Mixed Numbers (Step-by-Step)

 

Conclusion: How to Multiply Fractions

Multiplying fractions is an important math skill that you can master with a little bit of practice.

This guide shared a simple and effective 3-step strategy that you can use to solve any problem requiring you to multiply fractions together in any of the following scenarios:

  • multiplying fractions by other fractions

  • multiplying fractions by whole numbers

  • multiplying whole numbers by fractions

  • multiplying mixed fractions

  • multiplying mixed numbers

The good news is that the 3-step strategy shared in this guide can be used to solve problems for all of the above scenarios and can be summarized as follows:

  • Step One: Multiply the numerators together.

  • Step Two: Multiply the denominators together.

  • Step Three: See if the resulting fraction can be simplified or reduced.

The more practice you get using these three steps, the better at multiplying fractions you will become!

Keep Learning


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How to Divide Fractions in 3 Easy Steps

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How to Divide Fractions in 3 Easy Steps

How to Divide Fractions in 3 Easy Steps

Math Skills: How do you divide fractions by fractions, how do you divide fractions with whole numbers, and how to divide mixed fractions?

 

Free Step-by-Step Guide: How to Divide Fractions Step-by-Step Guide

 

Performing operations on fractions can be challenging. Once you have mastered how to add fractions and how to subtract fractions, the next step is learning how to multiply and how to divide fractions.

The following free guide specifically focuses on teaching you how to divide fractions in the following scenarios:

While dividing fractions may seem challenging at first glance, you can actually easily solve all three types of problems by using a simple 3-step method for dividing fractions, which you will learn and apply to several practice problems further down in this step-by-step guide.

Together, we will learn the Keep-Change-Flip method for how to divide fractions and use it to solve a variety of practice problems.

However, before we dive into working through any examples, let’s do a quick review of some key vocabulary terms and prerequisite skills that you will need to refresh in order to be successful with this new math skill.

Before we cover how to subtract fractions and work through a few examples, let’s do a fast recap of some key characteristics and vocabulary terms related to subtracting fractions.

Are you ready to get started?

How to Divide Fractions: Key Vocabulary

Since we will be using several math vocabulary terms in this guide, it is important that you are familiar with their meanings before you start working on the practice problems.

What is the numerator of a fraction?

The numerator of a fraction is the top number of the fraction. For example, for the fraction 2/3, the numerator is 2.

What is the denominator of a fraction?

The denominator of a fraction is the bottom number of the fraction. For example, for the fraction 2/3, the numerator is 3.

Pretty simple, right? Whenever we mention the numerator of a fraction, we are talking about the top number. On the other hand, whenever we mention the denominator of a fraction, we are talking about the bottom number. Figure 01 below illustrates the relationship.

 

Figure 01: In any fraction, the numerator is the top number and the denominator is the bottom number.

 

Next, let’s make sure that you understand the difference between fractions, whole numbers, and mixed numbers (also referred to as mixed fractions).

What is a whole number?

In math, a whole number is a number that is not a fraction. For example, 7, 23, and 100 are all whole numbers.

What is a fraction?

In math, a fraction is a number that represents a part of a whole number. For example, 1/2, 2/3, and 5/8 are all fractions.

What is a mixed number?

In math, a mixed number (or a mixed fraction) is a number that consists of both a whole number and a proper fraction. For example, 3 2/5 is a mixed number that represents the sum of 3 and 2/5.

Why is it important for you to understand the key characteristics and differences between these three types of numbers? Because, in this guide, you will learn how to work with dividing each type of number using a simple 3-step method.

 

Figure 02: What is a whole number? What is a fraction? What is a mixed fraction?

 

Now that you are familiar with all of the key vocabulary related to how to divide fractions, you are ready to work through some practice problems. Let’s start with learning how to divide fractions by other fractions.


How to Divide Fractions by Fractions

How to Divide Fractions by Fractions: Example #1

Example #1: 1/4 ÷ 1/4

Our first dividing fractions example is very simple, and you may already know the answer. In this case, we are taking the fraction 1/4 (one-fourth) and dividing it by 1/4 (one-fourth). So, we are dividing the same non-zero value by itself, which we should already know will be equal to 1.

Even though we already know what the answer should be, let’s go ahead and learn our 3-step method for dividing fractions to this first practice problem to see if it works as it should.

How to Divide Fractions in 3 Easy Steps

  • Step One: Keep the first fraction as is.

  • Step Two: Change the division sign to a multiplication sign.

  • Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

We will also be referring to this 3-step method as Keep-Change-Flip. Once you learn how to successfully follow these three simple steps, you can use them to solve any problem where you have to divide fractions!

Let’s go ahead and apply them to this first example: 1/4 ÷ 1/4

Step One: Keep the first fraction as is.

This first thing that you have to do is nothing at all. Simply leave the first fraction as is. So, 1/4 stays as 1/4.

Step Two: Change the division sign to a multiplication sign.

Next, take the division sign (÷) and change it to a multiplication sign (x) as follows:

  • 1/4 ÷ → 1/4 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

For this last step, take the second fraction and “flip” the position of the numerator and the denominator. So, 1/4 becomes 4/1 as follows:

  • 1/4 → 4/1

Now, we have used the Keep-Change-Flip method transform the original problem:

  • 1/4 ÷ 1/4 → 1/4 x 4/1

Figure 03 below illustrates how we used the keep-change-flip method to transform the original division problem into a multiplication problem.

 

Figure 03: How to Divide Fractions: Transform the original division problem into a multiplication problem using keep-change-flip.

 

Finally, we can solve this problem by multiplying these two fractions together. To do this, simply multiply the numerators together and the denominators together as follows:

  • 1/4 x 4/1 = (1x4) / (4x1) = 4/4 = 1

Final Answer: 1

When we multiply these two fractions together, we are left with (1x4) / (4x1) = 4/4 and we know that 4/4 can be reduced to 1, which we expected the answer to be when we first started this problem!

(Looking for some extra help with multiplying fractions, click here to access our free student guide).

Figure 04 below illustrates how we solved this problem after performing keep-change-flip on the original expression.

 

Figure 04: How to solve Example #1 after performing keep-change-flip on the original problem.

 

Confused? If so, that’s okay. The important thing is that you gain some experience with using keep-change-flip. Now let’s go ahead and apply it to another practice problem.


How to Divide Fractions by Fractions: Example #2

Example #2: 2/3 ÷ 4/5

For this second practice problem, we will again be using the 3-step method:

Step One: Keep the first fraction as is.

The first step, simply keep the first fraction 2/3 the same (i.e. you can just leave it as is).

Step Two: Change the division sign to a multiplication sign.

Next, take the division sign (÷) and change it to a multiplication sign (x) as follows:

  • 2/3 ÷ → 2/3 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Finally, flip the positions of the numerator and the denominator of the second fraction as follows:

  • 4/5 → 5/4

Again, these 3-steps can be referred to as keep-change-flip, and they are illustrated below in Figure 05:

 

Figure 05: Transform the original problem from Example #2 using Keep-Change-Flip

 

As you can see, we have transformed the original problem using keep change flip and we can now solve it as follows:

  • 2/3 x 5/4 = (2x5) / (3x4) = 10/12 = 5/6

Final Answer: 5/6

Remember, whenever you are multiplying two fractions together, you have to multiply the numerators together and then multiply the denominators together. In this example, we are left with (2x5)/(3x4) = 10/12, and, since 10 and 12 are both divisible by 2, we can reduce and express our final answer as 5/6.

Figure 06 below shows the complete process for solving this second example.

 

Figure 06: How to Divide Fractions Using the Keep-Change-Flip Method

 

Now, let’s go ahead and work through one more example of dividing a fraction by another fraction.


How to Divide Fractions by Fractions: Example #3

Example #2: 7/8 ÷ 11/12

Step One: Keep the first fraction as is.

As always, start by keeping the first fraction (7/8 in this example) as is.

Step Two: Change the division sign to a multiplication sign.

Next, change the division sign (÷) to a multiplication sign (x):

  • 7/8 ÷ → 7/8 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Now, flip the positions of the numerator and the denominator of the second fraction:

  • 11/12 → 12/11

The keep-change-flip process for Example #3 is shown in Figure 07 below:

 

Figure 07: How to transform a fractions division problem using keep-change-flip.

 

Now that have transformed the original problem, we can solve it as follows:

  • 7/8 x 12/11 = (7x12) / (8x11) = 84/88 = 21/22

Final Answer: 21/22

In this case, we end up with (7x12) / (8x11) = 84/88 and, since 84 and 88 are both divisible by 4, we can reduce and express our final answer as 21/22.

Figure 08 illustrates how we solved this problem.

 

Figure 08: How to Divide Fractions Using Keep-Change-Flip.

 

Next, we will learn how to divide fractions with whole numbers.


How to Divide Fractions with Whole Numbers

This next section will teach you how to divide a fraction by a whole number and how to divide a whole number by a fraction. We will again be using the keep-change-flip method to solve these kinds of problems. If you want a more in-depth review of how to use the keep-change-flip method, you can click here to revisit the previous section.

How to Divide a Fraction by a Whole Number: Example #1

Example #1: 3/7 ÷ 2

Ready for some good news? You can use the same keep-change-flip method from the previous section to solve these kinds of problems as well. However, there is one extra step involved. Whenever you want to divide a fraction by a whole number using keep-change-flip, you have to rewrite the whole number as a fraction by giving it a denominator of 1.

For this example, we can rewrite the whole number, 2, as a fraction as follows:

  • 2 → 2/1

These both mean the same thing! Now, we can say that solving the original problem is the same as solving 3/7 ÷ 2/1. And since this new problem is just dividing a fraction by another fraction, we can use the keep-change-flip method as follows:

Step One: Keep the first fraction as is.

For the first step, simply keep the first fraction, 3/7, as is.

Step Two: Change the division sign to a multiplication sign.

For the second step, change the division sign (÷) into a multiplication sign (x) as follows:

  • 3/7 ÷ → 3/7 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Finally, flip the positions of the numerator and the denominator of the second fraction as follows:

  • 2/1 → 1/2

The keep-change-flip process effectively transforms the division problem into an equivalent multiplication problem that is much easier to solve. This entire process is illustrated in Figure 09 below.

 

Figure 09: How to Divide a Fraction by a Whole Number: Rewrite the whole number as a fraction with a denominator of 1 and use the keep-change-flip method to solve.

 

Using the keep change flip method transforms the original division problem into an equivalent multiplication problem. To multiply two fractions together, simply multiply the numerators together and then multiply the denominators together as follows:

  • 3/7 x 1/2 = (3x1) / (7x2) = 3/14

Notice that the result, 3/14, can not be reduced. Therefore:

Final Answer: 3/14

The graphic in Figure 10 below details the entire process for solving this problem.

 

Figure 10: 3/7 x 1/2 = 3/14

 

In the next example, we will use the exact same process to divide a whole number by a fraction.


How to Divide a Whole Number by a Fraction: Example #2

Example #1: 9 ÷ 3/4

If we want to use the keep-change-flip method to divide a whole number by a fraction, then we will have to rewrite the whole number (9 in this case) as a fraction as follows:

  • 9 → 9/1

Now we can rewrite the original problem 9 ÷ 3/4 as 9/1 ÷ 3/4 (remember that these expressions are equivalent—i.e. they both mean the same thing). Now that we have two fractions being divided by each other, we can use keep-change-flip to solve.

Step One: Keep the first fraction as is.

Just like before, start by keeping the first fraction, 9/1, as is.

Step Two: Change the division sign to a multiplication sign.

Next, change the division sign (÷) into a multiplication sign (x) as follows:

  • 9/1 ÷ → 9/1 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Finally, flip the numerator and the denominator of the second fraction as follows:

  • 3/4 → 4/3

The entire process of using keep-change-flip to transform this problem is illustrated in Figure 11 below.

 

Figure 11: How to Divide a Whole Number by a Fraction: Start by rewriting the whole number as a fraction and then use keep-change-flip to solve.

 

Now we can solve the problem by multiplying these two fractions together as follows:

  • 9/1 x 4/3 = (9x4) / (1x3) = 36/3 = 12

Notice that the result, 36/3, can be reduced. Since both the numerator and denominator are divisible by 3, we can conclude that the final answer is 12/1 or just 12.

Final Answer: 12

The graphic in Figure 12 further illustrates how we solved this problem.

 

Figure 12: How to divide a whole number by a fraction using keep-change-flip

 

Now that you know how to divide a fraction by a whole number and how to divide a whole number by a fraction, let’s move onto the final section where you will learn how to divide mixed fractions.


How to Divide Mixed Fractions

The final section of the How to Divide Fractions guide will focus on how to divide mixed fractions and how to divide fractions with mixed numbers.

Again, we can solve all of these types of problems by using the keep-change-flip method (click here to revisit the previous section).

Let’s get started with our first example!

How to Divide Fractions with Mixed Numbers: Example #1

Example #1: 5/9 ÷ 3 1/3

Whenever you have to divide fractions with mixed numbers, you can use the keep-change-flip method to find the answer. However, before you can use keep-change-flip, you will have to convert the mixed number into an improper fraction first.

In this example, we have to convert the fraction 3 1/3 into an improper fraction (a fraction whose numerator is greater than its denominator).

We can rewrite 3 1/3 as 10/3 because:

  • 3 1/3 = 3/3 + 3/3 + 3/3 + 1/3 = 10/3

If you need more help with converting mixed numbers into improper fractions, we highly recommend checking out this free guide before moving forward.

Now, we can rewrite the original problem as follows:

  • 5/9 ÷ 3 1/3 → 5/9 ÷ 10/3

Both of these expressions are equivalent to each other. The key difference here is that the new expression allows us to use the keep-change-flip method to solve it as follows:

Step One: Keep the first fraction as is.

As always, simply keep the first fraction, 5/9, as is.

Step Two: Change the division sign to a multiplication sign.

Next, change the division sign (÷) to a multiplication sign (x) as follows:

  • 5/9 ÷ → 5/9 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Lastly, flip the positions of the numerator and the denominator of the second fraction as follows:

  • 10/3 → 3/10

Why are we doing this? Remember that the keep-change-flip method allows us to transform the original division problem into an equivalent multiplication problem that will be much easier to solve. This process is highlighted in Figure 13 below.

 

Figure 13: How to Divide Fractions with Mixed Numbers: Rewrite the mixed number as an improper fraction and then use keep-change-flip to solve.

 

From here, we can solve by multiplying these two fractions together as follows:

  • 5/9 x 3/10 = (5x3) / (9x10) = 15/90 = 1/6

Final Answer: 1/6

Figure 14 below illustrates how we were able to divide fractions with mixed numbers and solve this problem.

 

Figure 14: How to Divide Fractions with Mixed Numbers Explained

 

Now, let’s work through the final example of this guide where you will learn how to divide mixed fractions.


How to Divide Mixed Fractions: Example #2

Example #1: 6 1/2 ÷ 2 1/4

Just like the previous example, we can use the keep-change-flip method to solve this problem, but first we have to convert the mixed fractions in this problem into improper fractions.

In this case:

  • 6 1/2 = 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 1/2 = 13/2

  • 2 1/4 = 4/4 + 4/4 + 1/4 = 9/4

So, we can rewrite the original problem as:

  • 6 1/2 ÷ 2 1/4 → 13/2 ÷ 9/4

 

Figure 14: How to Divide Mixed Fractions: Start by rewriting any mixed fractions as improper fractions.

 

Again, if you need to review how to convert a mixed numbers into an improper fraction, we highly recommend checking out this free step-by-step guide.

Now, we have a new, yet equivalent, expression to be solved using keep-change-flip:

  • 13/2 ÷ 9/4

Step One: Keep the first fraction as is.

First, keep the first fraction, 13/2, as is.

Step Two: Change the division sign to a multiplication sign.

Second, change the division sign (÷) to a multiplication sign (x) as follows:

  • 13/2 ÷ → 13/2 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

And finally, flip the numerator and the denominator positions of the second fraction:

  • 9/4 → 4/9

 

Figure 15: How to Divide Mixed Fractions Explained

 

The last thing we have to do to solve this problem is multiply these two improper fractions together as follows:

  • 13/2 x 4/9 = (13x4) / (2x9) = 26/9 or 2 8/9

For this example, we are left we the improper fraction 26/9, which can not be reduced any further. You can also convert 26/9 into a mixed number, which would be 2 8/9. Both of these answers are equivalent.

Final Answer: 26/9 or 2 8/9

Figure 16 below shows how we found this final answer.

 

Figure 16: You will likely have to convert your final answer into a mixed number.

 

Conclusion: How to Divide Fractions

Dividing fractions can be a conceptually challenging math task, but learning how to use the keep-change-flip method can make the process much easier.

Whether you are dividing fractions with other fractions, fractions with whole numbers, whole numbers with fractions, or fractions with mixed numbers, the keep-change-flip method provides a simple three-step process for solving these types of problems.

The keep-change-flip method for dividing fractions can be summarized as follows:

  • Step One: Keep the first fraction as is.

  • Step Two: Change the division sign to a multiplication sign.

  • Step Three: Flip the position of the numerator and the denominator in the second fraction.

After you perform keep-change-flip, you can solve the problem by multiplying and reducing the result whenever possible.


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How to Round to the Nearest Thousandth—Step-by-Step Guide

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How to Round to the Nearest Thousandth—Step-by-Step Guide

How to Round to the Nearest Thousandth

Rounding to the Nearest Thousandth in 3 Easy Steps

 

Free Step-by-Step Guide: How to round to the nearest thousandth.

 

Learning how to correctly round numbers, especially numbers with decimals, is an important math skill that will help you to work with numbers, make accurate estimations, and solve problems.

Many students find rounding to be a relatively easy skill to learn when it comes to working with whole numbers, but many of those same students will struggle with rounding once decimals are involved. However, while rounding decimal numbers may seem trickier than rounding whole numbers, the process remains the same and learning how to round to the nearest thousandth decimal place is a math skill that every student can easily learn.

Ready to learn how to round to the nearest thousandth? This free step-by-step guide will show you how to round to the nearest thousandth by working through six different practice problems together. By working through each problem together, you will gradually learn everything you need to know about rounding to the nearest thousandth to the point that you will be able to solve decimal rounding problems with ease.

For this guide on rounding, you can work through each section in order, or you can use the quick links below to jump to a particular section of interest:

(Looking for help with rounding to the nearest tenth and rounding to the nearest hundredth?)

What is Rounding?

In math, the process of rounding involves taking a given number and rewriting it as a new number that serves as a close estimation of its actual value. Why? Because, mathematically speaking, doing so makes the original number easier to work with.

Consider a smoothie that costs $7.95. By rounding to the nearest whole number (or whole dollar in this case), you could say that the cost of a smoothie is $8. If you had to figure out the cost of 13 smoothies, without rounding, you would have to calculate 7.95 x 13 = ?, which isn’t exactly the easiest multiplication problem to solve in your head. On the other hand, if had to figure out the cost of 13 smoothies after rounding $7.95 to $8, you can determine close estimate of the actual cost simply by performing 8 x 13 = $104. So, you could say that the approximate cos of 13 smoothies would be $104.

  • Actual Cost: 7.95 x 13 = $103.35

  • Estimated Cost: 8.00 x 13 = $104.00

Notice how rounding made this problem much easier to solve and the difference between the actual cost and the estimated cost is relatively small.

The key takeaway here is that rounding a mathematical tool that you can use to estimate values and make them easier to work with and perform operations on.

 

Figure 01: The process of rounding involves taking a given number and rewriting it as a new number that serves as a close estimation of its actual value

 

Rounding Up vs. Rounding Down

Next, let’s run through a quick refresher on the difference between rounding up and rounding down.

You probably already know that, when it comes to rounding, the number 5 is a big deal. Why?

Rounding Rule: If the number directly to the right of the number you are rounding is greater than or equal to 5, then you will round up. Conversely, if the number directly to the right of the number you are rounding is less than or equal to 4, then you will round down.

As far as rounding rules go, this is the only true definition that you will need to remember if you want to learn how to successful round to the nearest thousandth. And, this rule will apply to any rounding problem you will come across, so make sure that you have a firm understanding of it before moving on.

Reminder:

  • If the number directly to the right of the number you are rounding is ≥ 5 → round up

  • If the number directly to the right of the number you are rounding is 4 → round down

Let’s consider two simple examples:

Example A: Round 128 to the nearest ten.

In this example, 2 is in the tens decimal place and the number 8 is directly to the right of it. Since 8 ≥ 5, you will have to round up the 2 as follows:

  • 128 → 130

Example B: Round 254 to the nearest ten.

In this example, 5 is in the tens decimal place and the number 4 is directly to the right of it. Since 4 ≤ 4, you will have to round down the 5 as follows:

  • 254 → 250

 

Figure 02: Whenever the number directly to the right of the number you are rounding is ≥ 5, you have to round up. Otherwise, round down.

 

3-Step Process: How to Round to the Nearest Thousandth

Now that you understand what it means to round a number and the difference between rounding up and rounding down, you are ready to learn how to round to the nearest thousandth and work through some practice problems.

For all of the rounding to the nearest thousandth examples in this guide, we will be using the following 3-step process for rounding to the nearest thousandth:

  • Step #1: Locate and underline the value in the thousandths place value slot

  • Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

  • Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

It’s ok if this 3-step process seems complicated at first glance. After working through a few examples, you will become much more comfortable with using these three steps to solve decimal rounding problems with ease


Example #1: Round to the Nearest Thousandth: 5.3641

Let’s go ahead and dive into our first example where we are tasked with rounding 5.3641 to the nearest thousandth.

We will solve this problem (and all of the practice problems in this guide) using the previously described 3-step process as follows:

Step #1: Locate and underline the value in the thousandths place value slot

For the number 5.3641, there are four numbers to the right of the decimal place. The third number to the right of the decimal place will always be the thousandths place value slot, which, in this example, is the number 4.

Locating and underlining the value in the thousandths place vale slot is illustrated in Figure 03 below.

 

Figure 03: How to round to the nearest thousandth: The first step is to identify the thousandths place value slot.

 

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

Next, take a look at the number directly to the right of the 4 in the thousandths place value slot.

In this example, that number is 1, which is ≤ 4.

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

Since the number directly to the right of the 4 in the thousandths place value slot is 1, which is ≤ 4, you will have to round down.

In this case, rounding down means that the 1 to the right of the 4 in the thousandths place value slot becomes a zero and effectively disappears, which leaves us with:

Final Answer: 5.3641 rounded to the nearest thousandth is 5.364

The complete process of solving this first example is shown in Figure 04 below:

 

Figure 04: When rounding down, the number to the right of the thousandths decimal slot becomes a zero and disappears.

 

Example #2: Round to the Nearest Thousandth: 5.3648

For the next example, you will notice that the number in question is very similar to the previous example. In this case, the only difference is that the final number is an 8 rather than a 1.

How will this difference effect the final answer? Let’s apply our 3-step process and see:

Step #1: Locate and underline the value in the thousandths place value slot

For this example, the number 4 is in the thousandths place value slot as shown in Figure 05 below.

 

Figure 05: How to round to the nearest thousandth: Start by identifying the value in the thousandths decimal slot.

 

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

In this example, the number directly to the right of the 4 in the thousandths place value slot is 8.

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

The number directly to the right of the 4 in the thousandths place value slot is 8, and 8≥ 5, so this time we will be rounding up.

When rounding up, you will add one to the value in the thousandths place value slot (4 in this example) and all numbers to the right of it will disappear.

Final Answer: 5.3648 rounded to the nearest thousandth is 5.365

This process of solving Example #2 is illustrated in Figure 06 below.

 

Figure 06: 5.3648 rounded to the nearest thousandth is 5.365

 

Before moving onto more practice problems, let’s take a closer look at the differences between rounding the numbers in Example #1 and Example #2 to the nearest thousandth:

  • Example #1: 5.3641 → 5.364 (we rounded down)

  • Example #2: 5.3648 → 5.365 (we rounded up)

The graphic in Figure 07 below further highlights the differences between how we solved these first two examples (namely, the difference between solving by rounding down and solving by rounding up).

 

Figure 07: Examples of rounding down vs. rounding up.

 

Example #3: Round to the Nearest Thousandth: 1.27025

Moving onto this next example, you will notice that the number 1.27025 includes five digits to the right of the decimal point. However, whenever you are rounding to the nearest thousandth, you will only need to first four digits and anything beyond that can be ignored.

To see this process in action, let’s go ahead and apply our 3-step process for rounding to the nearest thousandth.

Step #1: Locate and underline the value in the thousandths place value slot

For the number 1.27025, the number 0 is in the thousandths place value slot, as shown in Figure 08 below.

 

Figure 08: Remember that you only need the first four digits the right of the decimal point to round a number to the nearest thousandth. Anything beyond that can be ignored.

 

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

Next, notice that 0 is in the thousandths place value slot and the number directly to the right of it is a 2, which is ≤ 4.

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

Since 2 ≤ 4, we will be rounding down to solve this problem as is shown in Figure 09 below:

Final Answer: 1.27025 rounded to the nearest thousandth is 1.270

 

Figure 09: 1.27025 rounded to the nearest thousandth is 1.270

 

Example #4: Round to the Nearest Thousandth: 24.3759414

Again, we can solve this problem by applying our 3-step process. Just remember that you can ignore any numbers that come after the fourth number to the right of the decimal point.

Step #1: Locate and underline the value in the thousandths place value slot

For the number 24.3759414, the number 5 is in the thousandths place value slot.

 

Figure 10: The number 5 is in the thousandths place value slot.

 

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

The number directly to the right of the 5 is 9, and 9 ≥ 5.

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

Since 9 ≥ 5, you must round it up to solve this problem and conclude that:

Final Answer: 24.3759414 rounded to the nearest thousandth is 24.376

Figure 11 below illustrates the entire 3-step process for rounding Example #4 to the nearest thousandth.

 

Figure 11: 24.3759414 rounded to the nearest thousandth is 24.376

 

Example #5: Round to the Nearest Thousandth: 18.34951

Are you starting to get the hang of it? Let’s continue onto another example.

Step #1: Locate and underline the value in the thousandths place value slot

For the number 18.34951, the digit in the thousandths place value slot is 9.

 

Figure 14: How to Round to the nearest Thousandth: The digit in the thousandths place value slot is 9.

 

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

Next, the number directly to the right is 5, and 5 ≥ 5.

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

Since 5 ≥ 5, we know that we have to take the 9 in the thousandths place value slot and round it up. But how do you round up the number 9 without turning it into a 10?

Rule: Whenever you are rounding up the number 9, you have to turn it into a zero and add one to the number directly to the left of the 9.

Figure 13 below illustrates the application of this rule being used to solve Example #5.

Final Answer: 18.34951 rounded to the nearest thousandth equals 18.350

 

Figure 13: Whenever you are rounding up the number 9, you have to turn it into a zero and add one to the number directly to the left of the 9.

 

Example #6: Round to the Nearest Thousandth: 0.023499

You made it to the final example! To solve this last problem, we will again rely on our 3-step process as follows:

Step #1: Locate and underline the value in the thousandths place value slot

In this example, 0.023499, the number 3 is in the thousandths place value slot.

 

Figure 14: Reminder: When it comes to rounding to the nearest thousandth, you can ignore any additional numbers after the fourth digit to the right of the decimal point.

 

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

Notice that the number directly to the right of the 3 is a 4.

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

Since 4 ≤ 4, we know that we have to round down to solve this problem.

Final Answer: 0.023499 rounded to the nearest thousandth is 0.023

 

Figure 15: Rounding 0.023499 to the nearest thousandth.

 

Conclusion: Round to the Nearest Thousandth

Rounding numbers, especially decimals, is an extremely important and useful math skill that helps students to estimate numbers and make calculations with them.

This guide specifically focused on rounding to the nearest thousandth, where you learned and applied a simple 3-step method to rounding any number to the nearest thousandth decimal place:

Step #1: Locate and underline the value in the thousandths place value slot

Step #2: Identify if the number directly to the right is ≥ 5 or ≤ 4

Step #3: If the number directly to the right is ≥ 5, round up the number in the thousandths place value slot. If the number directly to the right is ≤ 4, round down the number in the thousandths place value slot to zero.

You can use this 3-step process to solve any problem where you have to round a given number to the nearest thousandth! So, it should be no surprise that we were able to use it to solve all six practice problems in this guide and make the following conclusions:

  • 5.3641 → 5.364

  • 5.3648 → 5.365

  • 1.27025 → 1.270

  • 24.3759414 → 24.376

  • 18.34951 → 18.350

  • 0.023499 → 0.023

Need some extra practice? If so, we strongly recommend that you go back and work through the practice problems in this guide again. The more that you practice, the more comfortable you will become with the 3-step process. And, if you need some additional practice beyond this guide, check out the free rounding worksheets and answer keys available on our free math worksheet libraries.

Keep Learning:

How to Round to the Nearest Hundredth (Step-by-Step Guide)

Continue your rounding journey by learning how to round to the nearest hundredth.


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How to Round to the Nearest Hundredth—Step-by-Step Guide

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How to Round to the Nearest Hundredth—Step-by-Step Guide

How to Round to the Nearest Hundredth

Step-by-Step Guide: Rounding to the Nearest Hundredth in 3 Easy Steps

 

Free Step-by-Step Guide: How to round to the nearest hundredth.

 

Knowing how to round numbers, especially numbers involving decimals, is an incredibly useful math skill that will help you to work large and small numbers and estimate their values.

While rounding whole numbers can be relatively straightforward, the process gets a little trickier when decimals are involved. However, this guide will make sure that you are familiar with key vocabulary and our easy-to-follow three-step method for rounding numbers to the nearest hundredth. Once you learn to apply this method, you can use it to solve any problem where you are tasked with rounding to the nearest hundredth.

Are you ready to get started? The following free guide will teach you everything you need to know about rounding to the nearest hundredth including step-by-step explanations of solving several practice problems.

While we highly recommend that you read each section in order, you can use the quick links below to jump to a specific topic or section:

(Looking for help with rounding to the nearest tenth and rounding to the nearest thousandth?)

What does rounding a number mean?

Rounding a number is the process of rewriting a number to a value that closely estimates its actual value so that is easier to understand and perform operations on.

For example, if a large coffee costs $4.97, you could estimate the cost to be $5 even (this would be an example of rounding to the nearest whole number). If someone asked you how much money you would need to purchase six coffees, you could easily estimate the cost to be $30 (since 5 x 6 =30), rather than having to figure out the value of 4.97 x 6.

So, rounding is just a method of making larger or small numbers easier to work with.

 

Figure 01: An example of rounding is estimating that the cost of a $4.97 cup of coffee to be $5 since it is an easier number to work with.

 

When do you round down and when do you round up?

Now that you understand what rounding means, it is important that you know the difference between situations when you have to round up and when you have to round down.

In the case of rounding, the number 5 is extremely significant.

RULE: If the number to the right of the number you are rounding is 5 or greater, then you must round up. If the number to the right of the number you are rounding is 4 or less, then you must round down.

This rule applies to rounding any whole number or decimal number. To help you to remember this rule, you can use the “rounding hill” shown in Figure 02 below to help you remember when to round up and when to round down.

  • If digit to the right of the number being rounded is 4 or less → round down

  • If digit to the right of the number being rounded is 5 or greater → round up

For example, if you wanted to round 58 to the nearest ten, the rounded answer is 60 since 8 (the number to the right of the tens digit) is 5 or greater, meaning you have to round up.

  • 58 8 is 5 or greater, so round up 60

On the other hand, if you wanted to round 43 to the nearest ten, the result would be 40 since 3 (the number to the right of the tens digit) is 4 or less, meaning you have to round down.

  • 43 3 is 4 or less, so round down 40

 

Figure 02: This illustration of a “rounding hill” can help you to remember when to round up and when to round down.

 

What does rounding to the nearest hundredth mean in terms of place value?

The last key topic that we have to review before we start working on some examples of rounding to the nearest hundredth is place value.

Definition: Place Value is the numerical value that a digit has based on its position in the number.

Consider the number 472.893

We can think of the number 472.893 as the sum of:

  • 4 hundreds

  • 7 tens

  • 2 ones

  • 8 tenths

  • 9 hundredths

  • 3 thousandths

Just like the “rounding hill” in Figure 02, you can use a place value chart, as shown in Figure 03 below, as a visual tool to help you to correctly identify the place values of digits in any given number.

▶ FREE DOWNLOAD: Blank Decimal Place Value Chart (PDF File)

Before moving forward, make sure that you have a strong understanding of place value and that you can correctly identify place values, especially for values to the right of a decimal sign.

 

Figure 03: You can use a place value chart to help you to correctly identify the place value of each digit in a number.

 

Keep Learning: Where is the hundredths place value in math?

Since this guide focuses on rounding to the nearest hundredth, here are a few examples of identifying the hundredths and thousandths place value digit for the following numbers.

  • 5.279 7 is in the hundredths decimal place, 9 is in the thousandths decimal place

  • 76.105 0 is in the hundredths decimal place, 5 is in the thousandths decimal place

  • 0.444 4 is in the hundredths decimal place, 4 is in the thousandths decimal place

  • 2,000.018 1 is in the hundredths decimal place, 8 is in the thousandths decimal place

 

Figure 04: How to identify the hundredths and thousandths decimal places in a given number.

 

How to Round to the Nearest Hundredth using 3 Simple Steps

Ready to work through some practice problems focused on rounding to the nearest hundredth?

For all of the practice problems in this guide, you can use the following 3-step process for rounding to the nearest hundredth:

  • Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

  • Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

  • Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

If these three steps seam confusing at first, that’s okay. They will make more sense once you get some experience applying them to the following practice problems.


Example #1: Round to the Nearest Hundredth: 4.253

Starting off with our first example, we are tasked with rounding the number 4.253 to the nearest hundredth.

We can solve this problem by applying the 3-step method as follows:

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

For the number 4.253, the 3 is in the thousandths decimal place slot (and there are no additional numbers to the right of it).

 

Figure 05: For the number 4.253, the number 3 is in the thousandths place value slot.

 

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

For this example, 3 is in the thousandths place value slot and 3 is 4 or smaller, so we will have to round down in the third and final step.

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

In the last step, we determined that the value in the thousandths place value slot, 3, is 4 or smaller and that we have to round down. When rounding down, we turn that 3 in the thousandths place value slot into a zero, which effectively makes it disappear. Now, we can conclude that:

Final Answer: 4.254 rounded to the nearest hundredth is 4.25

The final answer to Example 1 (and the steps to solving it) is displayed in Figure 06 below.

 

Figure 06: When rounding down, the number in the thousandths decimal spot becomes a zero and disappears.

 

Example #2: Round to the Nearest Hundredth: 4.257

Notice that Example #2 is very similar to Example #1. The only difference is that, in this example, the value of the number in the thousandths place value slot is a 7 (rather than a 3).

Let’s go ahead and apply our 3-step method to see how this difference affects our answer.

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

For the number 4.257, the 7 is in the hundredths place value slot as illustrated in Figure 07 below.

 

Figure 07: The thousandths place value slot is three digits to the right of the decimal point.

 

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

As previously stated, for this example, the value of the number in the thousandths place value slot is a 7, which is 5 or larger.

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

Since the value in the thousandths place value slot is 5 or larger, we have to round up to solve this problem. When rounding up, we have to add one to number in the tenths place value slot (the number directly to the left of the number in the thousandths place value slot) and “zero out” the number in the thousandths place value slot.

Final Answer: 4.257 rounded to the nearest hundredth is 4.26

The entire process of solving this second example is illustrated in Figure 08 below.

 

Figure 08: 4.257 rounded to the nearest thousandth is 4.26.

 

Before we move onto more practice problems, Figure 09 below compares the first two examples. Be sure that you understand the difference between rounding up and rounding down before moving on.

 

Figure 09: Comparing Example #1 (rounding down) and Example #2 (rounding up). What do you notice?

 

Example #3: Round to the Nearest Hundredth: 88.7309

For this third example, notice that there is a digit in the ten-thousandths decimal place (the value four digits to the right of the decimal point). While this number, 88.7309 is larger than the numbers in the first two examples, you can still use the 3-step method for rounding to the nearest hundredth to solve it.

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

For the number 88.7309, the thousandths place value digit (the number three digits to the right of the decimal point) is 0. Remember that you can ignore any numbers to the right of the digit in the thousandths place value slot (which is the 9 in this example).

For the sake of rounding correctly, you can ignore the 9 and think of this number as 88.730.

 

Figure 10: Remember that you can ignore any numbers to the right of the digit in the thousandths place value slot.

 

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

Next, notice that 0 is in the thousandths place value slot. Clearly, 0 is 4 or smaller.

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

Since 0 is 4 or smaller, we will have to round down. Since 0 is already 0, we can just make it disappear and make the following conclusion:

Final Answer: 88.7309 rounded to the nearest hundredth is 88.73

This final answer is shown in Figure 11 below.

 

Figure 11: 88.7309 rounded to the nearest hundredth is 88.73.

 

Example #4: Round to the Nearest Hundredth: 29.48736

Similar to the previous example, 29.48736 includes numbers the right of the thousandths decimal place. Remember that you can ignore these numbers and use the three steps to solve this problem as follows:

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

For the number 29.48736, the number 7 is in the thousandths place value slot.

 

Figure 12: When rounding to the nearest hundredth, the number in the thousandths place value slot will determine if you have to round up or down.

 

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

Since 7, the number in the thousandths place value slot, is 5 or larger, we will have to round up in step three.

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

To round this number to the nearest hundredth, you must add one to the 8 in the tenths place value slot and zero out the 7.

Final Answer: 29.48736 rounded to the nearest hundredth is 29.49

The complete three-step process for solving example #5 is shown in Figure 13 below.

 

Figure 13: 90.352 rounded to the nearest tenth is equal to 90.4

 

Example #5: Round to the Nearest Hundredth: 8.495

By now, you should be a bit more comfortable with rounding to the nearest hundredth. Let’s continue on to work through two more examples where we will gain more experience using the 3-step method.

For this next example, we have to round the number 8.495 to the nearest hundredth.

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

For the number 9.495, the digit in the thousandths place value slot is 5, as shown in Figure 14 below.

 

Figure 14: How to Round to the nearest Hundredth: When the digit in the thousandths place value slot is 5 or larger, you have to round up.

 

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

Next, we can see that 5 (digit in the thousandths place value slot) is indeed 5 or larger.

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

Since 5 is 5 or larger, we will have to round up. The number directly to the left of the thousandths digit is a 9, so how do we round it up without turning it into a double-digit number? In the case of rounding up the number 9, you must turn it into a zero and add one to the number directly to its left (this process is illustrated in Figure 15 below).

Final Answer: 8.495 rounded to the nearest hundredth equals 8.50

 

Figure 15: 8.495 rounded to the nearest hundredth equals 8.50

 

Example #6: Round to the Nearest Hundredth: 64.01408

Here is our final practice problem for rounding to the nearest hundredth!

To solve it, let’s go ahead and apply our 3-step method as follows:

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

For this last problem, the digit in the thousandths place value slot is 4, as shown below in Figure 16. Remember that all of the digits to the right of the 4 can be ignored.

 

Figure 16: Remember that, when it comes to rounding to the nearest tenth, you can ignore any additional numbers that come after the digit in the thousandths decimal slot.

 

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

Notice that the value in the thousandths place value slot is a 4, which is 4 or smaller.

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

Since the value in the thousandths place value slot is 4 or smaller, you can round it down to zero. Therefore, the 4 will disappear and we are left with the following result:

Final Answer: 64.01408 rounded to the nearest hundredth is 64.01

 

Figure 17: 64.01408 rounded to the nearest hundredth is 64.01

 

Conclusion: How to Round to the Nearest Hundredth

In math, it is important to know how to estimate and round numbers to make them easier to work with. This skill is especially important when it comes to working with decimal numbers.

By working through this step-by-step tutorial on rounding numbers to the nearest hundredth, you learned a simple 3-step process that you can use to round any number to the nearest hundredth. The 3-steps outlined in this guide are as follows:

Step One: Identify the value in the thousandths decimal place and ignore all numbers to the right of it

Step Two: Determine if the value in the thousandths decimal place is 5 or larger or 4 or smaller

Step Three: If the value in the thousandths decimal place is 5 or larger, round the number directly to the left (the value in the hundredths decimal place) up. If the value in the thousandths decimal place is 4 or smaller, round it down to zero.

Once you understand how to correctly apply these three steps, you can use them to solve any problem that requires you to round to the nearest hundredth. Using this method, we solved six different rounding practice problems where we had to round a given number to the nearest hundredth. Here is a quick review of our results:

  • 4.253 → 4.25

  • 4.257 → 4.26

  • 88.7309 → 88.73

  • 29.48736 → 29.49

  • 8.495 → 8.50

  • 64.01408 → 64.01

Need more help? If so, we suggest going back and working through this step-by-step guide again (practice makes perfect after all). You can also gain some more rounding practice by downloading some free topic-specific worksheets available on our free math worksheet libraries.

Keep Learning:

How to Round to the Nearest Thousandth (Step-by-Step Guide)

Continue your rounding journey by learning how to round to the nearest thousandth.


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How to Round to the Nearest Tenth—Step-by-Step Guide

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How to Round to the Nearest Tenth—Step-by-Step Guide

How to Round to the Nearest Tenth

Step-by-Step Guide: Rounding to the Nearest Tenth in 3 Easy Steps

 

Free Step-by-Step Guide: How to round to the nearest tenth.

 

Learning and understanding how to round numbers is an important and useful math skill that makes working with large numbers faster and easier.

When it comes to rounding decimals, learning how to round the nearest tenth decimal place is a pretty straightforward process provided that you understand a few vocabulary terms, the meaning of place value, and some simple procedure.

This free Step-by-Step Guide on Rounding to the Nearest Tenth will teach you everything you need to know about how to round a decimal to the nearest tenth and it cover the following topics:

Now, lets begin learning how to round to the nearest tenth by recapping some important math vocabulary terms and concepts.

(Looking for help with rounding to the nearest hundredth and rounding to the nearest thousandth?)

What is rounding in math?

In math, rounding is the process of approximating that involves changing a number to a close value that is simpler and easier to work with. Rounding is done by replacing the original number with a new number that serves as a close approximation of the original number.

For example, if a new pair of basketball sneakers costs $99.88, you could use rounding to conclude that you will need $100 to purchase the sneakers. In this example, you would be rounding to the nearest whole dollar and the purpose of rounding would be to replace the actual cost of “ninety-nine dollars and eight-eighty cents” with an approximated value of “one hundred dollars,” since it is simpler and easier to work with.

 

Figure 01: You could use rounding to say that a pair of sneakers that actually costs $99.88 has an approximate cost of $100, since one hundred is simpler and easier to work with.

 

As shown in Figure 01 above, $100 is simpler and easier to work with than $99.88. So, if you had to estimate the cost of 7 pairs of basketball shoes, you could easier estimate that the cost would be $700 (since 7 x 100 = 700).

What is the significance of 5 when it comes to rounding?

The next important thing to remember when it comes to rounding is the significance of the number 5. When you first learn how to perform simple rounding, you may use a visual aid called a rounding hill as shown in Figure 02 below. A rounding hill shows how, when it comes to rounding, if whatever digit you are rounding is less than 5 (4 or less), you will round down. If whatever digit you are rounding is 5 or greater, you will round up. So, 5 is the cutoff for rounding up in any rounding scenario.

  • If digit to the right of the number being rounded is 4 or less → round down

  • If digit to the right of the number being rounded is 5 or greater → round up

For example, if you wanted to round 17 to the nearest ten, the result would be 20 since 7 is 5 or greater and you would have to round up.

  • 17 7 is 5 or greater, so round up 20

Conversely, if you wanted to round 13 to the nearest ten, the result would be 10 since 3 is 4 or less and you would have to round down.

  • 13 3 is 4 or less, so round down 10

 

Figure 02: The Rounding Hill illustrates the significance of 5 and how you can determine when to round up and when to round down.

 

What does rounding to the nearest tenth mean in terms of place value?

Now that you know what rounding is and when to round up or round down, the final concept that we need to review is place value.

In math, place value refers to the numerical value that a digit has by virtue of its position in the number.

For example, consider the number 3.57.

We can think of the number 3.57 as the sum of 3 ones, 5 tenths, and 7 hundredths.

A useful tool for visualizing place value is called a place value chart, where each place value has its own slot so you can clearly identify a given digits place value. Figure 03 below shows the number 3.57 within a place value chart, where you can clearly see that 3 is in the ones place, 5 is in the tenths place, and 7 is in the hundredths place.

▶ FREE DOWNLOAD: Blank Decimal Place Value Chart (PDF File)

 

Figure 03: A place value chart is a useful tool for identify each digit’s place value, especially when you are dealing with decimals.

 

If you want to learn how to round to the nearest tenth, then you will need to be able to correctly identify the place value of the tenths and hundredths place value, otherwise you will struggle to correctly round a decimal to the nearest tenth (more on why this is the case later on in this guide).

Keep Learning: Where is the hundredths place value in math?

Here are a few more examples of correctly identifying the tenths and hundredths decimal places:

  • 4.12 1 is in the tenths decimal place and 2 is in the hundredths decimal place

  • 52.783 7 is in the tenths decimal place and 8 is in the hundredths decimal place

  • 0.3333 3 is in the tenths decimal place and 3 is in the hundredths decimal place

  • 488.60 6 is in the tenths decimal place and 0 is in the hundredths decimal place

 

Figure 04: Examples of identifying the tenths and hundredths decimal place for 4.12, 52.783, 0.3333, and 488.6

 

How to Round to the Nearest Tenth in 3 Easy Steps

Now you are ready to work through a few examples where you have to round to the nearest tenth using our easy 3-step method, which works as follows:

  • Step One: Identify the value in tenths place value slot and the hundredths place value slot

  • Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

  • Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

Let’s continue on to using these three steps to several practice problems.


Example #1: Round to the Nearest Tenth: 8.63

This first example is pretty simple. You are tasked with rounding to the nearest tenth the number 8.63.

Let’s go ahead and apply our 3-step method to solving this problem:

Step One: Identify the value in tenths place value slot and the hundredths place value slot

In this case, 6 is in the tenths place value slot and 3 is in the hundredths place value slot as shown in Figure 05 below.

 

Figure 05: For the number 8.63, 6 is in the tenths place value slot and 3 is in the hundredths place value slot.

 

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

For this example, 3 is in the hundredths place value slot. Since 3 is less than 5, we will have to round down in the final step.

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

As determined in step two, we will be rounding the hundredths place value digit, which is 3 in this example, down to zero. This effectively means that, when rounding to the nearest tenth, you must remove the hundredths value digit entirely and make the following conclusion:

Final Answer: 8.63 rounded to the nearest tenth is 8.6

This final result is illustrated in Figure 06 below. Now, let’s move onto a second example where you will have to round up to get your final answer.

 

Figure 06: Step One: Split the cubic polynomial into two groups

 

Example #2: Round to the Nearest Tenth: 32.87

For this next example, you can use the same 3-step approach to determine what is 32.8 rounded to the nearest tenth as follows:

Step One: Identify the value in tenths place value slot and the hundredths place value slot

For the number 32.87, 8 is in the tenths place value slot and 7 is in the hundredths place value slot as shown in Figure 07.

 

Figure 07: Rounding to the nearest tenth: The first step is to identify the digits in the tenths and hundredths place value slots.

 

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

For the second example, 7 is in the hundredths place value slot. Since the number 7 is greater than 5, we will have to round up in the last step.

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

We have already determined that finding 32.87 rounded to the nearest tenth will require rounding up. In this case, the 8 in the tenths decimal place will round up to a 9 and the hundredths decimal place will disappear.

Final Answer: 32.87 rounded to the nearest tenth is 32.9

This final answer is shown in Figure 08 below.

 

Figure 08: 32.87 rounded to the nearest tenth is 32.9

 

Example #3: Round to the Nearest Tenth: 119.308

Notice that this example includes a digit in the thousandths decimal place. While this is a larger number than the previous two examples, you can still use the 3-step process to find the value of 119.308 rounded to the nearest tenth.

Step One: Identify the value in tenths place value slot and the hundredths place value slot

In this example, for the number 119.308, 3 is in the tenths decimal place value slot, 0 is in the hundredths place value slot, and 8 is in the thousandths place value slot (although the 8 will not have any effect on how you solve this problem, and you can actually ignore it entirely and still correctly round 119.308 to the nearest tenth).

 

Figure 09: To find the value of 119.308 rounded to the nearest tenth, you only need to worry about the values in the tenths and hundredths place value slots (anything after that does not matter).

 

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

Continuing on, lets focus on the fact that 0 is in the hundredths place value slot for this third example.

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

Since 0 is less than 5, we will have to round it down to—zero. And since zero is already zero, all that you have to do is make it disappear entirely and conclude that:

Final Answer: 119.308 rounded to the nearest tenth is 119.3

This final answer is shown in Figure 10 below.

 

Figure 10: How to round to the nearest tenth: 119.308 can be rounded to 119.3

 

Example #4: Round to the Nearest Tenth: 90.352

Just like the last example, 90.352 includes a digit in the thousandths decimal place. And, just like the last example, you can ignore that digit entirely and apply the same 3-step method as follows:

Step One: Identify the value in tenths place value slot and the hundredths place value slot

The place value slots for 90.352 are as follows: 3 is in the tenths place value slot and 5 is in the hundredths place value slot. Again, you can ignore the 2 in the thousandths place value slot.

 

Figure 11: How to round to the nearest tenth: start by identifying the values of the tenths and hundredths place value digits

 

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

For the second step, our focus is on the 5 in the hundredths place value slot.

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

Since 5 is equal to 5 or greater, we will have to round up. Remember that 5 is the cutoff for rounding up, so this is an example where the number just meets the requirements for rounding up instead of down.

Final Answer: 90.352 rounded to the nearest tenth is 90.4

The entire process for solving example #4 is illustrated in Figure 12 below.

 

Figure 12: 90.352 rounded to the nearest tenth is equal to 90.4

 

Example #5: Round to the Nearest Tenth: 149.96

Are you starting to get the hang of using the three-step process to round numbers to the nearest tenth? Let’s try rounding 149.96 to the nearest tenth and find out:

Step One: Identify the value in tenths place value slot and the hundredths place value slot

For this fifth example, the digit in the tenths place value slot is 9 and the digit in the hundredths place value slot is 6, as shown in Figure 13 below.

 

Figure 13: The digit in the tenths place value slot is 9 and the digit in the hundredths place value slot is 6.

 

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

Moving on, note that the digit in the hundredths place value slot is 6, which is 5 or larger.

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

Since 6 is equal to 5 or greater, we will have to round up. However, notice that the digit in the tenths place value slot is a 9, which can not be rounded up to the next digit. In this case, the 9 will become a zero and the digit that gets rounded up is the one in the ones place value slot (the number directly to the left of the decimal point).

So, when you round 149.96 to the nearest tenth, the 9 becomes a zero and the number 149 gets rounded up to the next whole number as follows:

Final Answer: 149.96 rounded to the nearest tenth equals 150.0

 

Figure 14: 149.96 rounded to the nearest tenth is 150.0

 

Example #6: Round to the Nearest Tenth: 3.0499

Now let’s work through one final example of rounding a number to the nearest tenth.

Remember that you only need to know the digits in the tenths and hundredths place value slots to round correctly, and you can ignore any additional numbers.

Step One: Identify the value in tenths place value slot and the hundredths place value slot

For this final example, the digit in the tenths place value slot is 0 and the digit in the hundredths place value slot is 4, as illustrated in Figure 15 below.

 

Figure 15: Remember that, when it comes to rounding to the nearest tenth, you can ignore any additional numbers that come after the digit in the thousandths decimal slot.

 

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

Just as we did in all of the previous examples, the second step requires you to identify the value of the hundredths place value digit. For the number 3.0499, this value is 4.

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

4, the digit in the hundredths place value slot, is less than 5, so we will be rounding down. So, the disappears and the 0 in the tenths place value slot stays a 0 since it can not be rounded down any further.

Therefore, we can conclude that:

Final Answer: 3.0499 rounded to the nearest tenth equals 3.0

 

Figure 16: 3.0499 rounded to the nearest tenth is 3.0

 

How to Round to the Nearest Tenth: Conclusion

Rounding is an important math skill that every student must learn at some point. While rounding integers is relatively simple, the process, while similar, gets trickier when decimals are involved.

This step-by-step guide focused on teaching you how to round numbers to the nearest tenth (i.e. to the nearest tenth decimal place). By using the following 3-step method, you can successfully round any number involving decimals to the nearest tenth:

Step One: Identify the value in tenths place value slot and the hundredths place value slot

Step Two: Determine if the value in the hundredths place value slot is 5 or larger or 4 or smaller

Step Three: Round the value in the tenths place value slot up or down depending on the result from step two

This method will work for rounding any number to the nearest tenth. To recap, we used this method to solve the following examples where we were given a decimal number and tasked with rounding it to the nearest tenth:

  • 8.63 → 8.6

  • 32.87 → 32.9

  • 119.309 → 119.3

  • 90.352 → 90.4

  • 149.96 → 150.0

  • 3.0499 → 3.0

If you need more practice, we recommend working through the six practice problems in this guide again and/or working through the free rounding practice worksheets available on our free math worksheet libraries.

Keep Learning:

How to Round to the Nearest Hundredth (Step-by-Step Guide)

Continue your rounding journey by learning how to round to the nearest hundredth.


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