Free Printable Ruler with Fractions

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Free Printable Ruler with Fractions

Free Printable Ruler with Fractions

Free Printable Ruler with Fractions

Are you in need of a ruler with fractions to help you make exact measurements?

If so, you can use the text link below to download your free printable ruler with fractions as a PDF file. The pdf includes multiple rulers that you can cut out using a scissor and then use to make accurate measurements to the nearest eighth of an inch.

Click Here to Download Your Free Printable Ruler with Fractions

Preview: Ruler with Fractions (Image: Mashup Math)

Printing Instructions: To ensure that your rulers print out to exact proportions, it is essential that you print on standard US Letter Paper (8.5x11 inches) and that your printer’s settings are correctly assigned before you print the ruler with fractions pdf file. Before you print, make sure that your printer settings are set to portrait orientation (not landscape) and make sure that the scale is set to 100% size. Inputting the correct settings will ensure that the printable ruler will be exactly six inches long with perfect proportions. Note that many printers have a default “Fit to Page” print setting that will likely alter the scale of the printed ruler, making it an inaccurate measuring tool. You can verify whether or not your printed ruler is accurate by testing it against a standard ruler.

See the graphic in Figure 01 below for more detailed printer instructions.

 

Figure 01: Printable Rulers with Fractions Printing Instructions

 

Free Printable Ruler with Fractions: How to Use a Ruler

You can use the free printable ruler with fractions above to make exact measurements the same way that you would a typical wooden, metal, or plastic ruler.

Simply follow the printing instructions above to print out the free ruler with fractions PDF and then use a scissor to cut out one of the rulers and then follow the instructions below to start making measurements:

Once you have your ruler completely cut out, start by familiarizing yourself with the measurement lines on the ruler face. The longest lines mark the inch segments and they range from 0 to 6. In between each one inch segments there are 7 shorter lines that each represent fractions of an inch (one-eight or 1/8 to be precise). The line directly halfway between each one inch marker is the half-inch mark, followed by the quarter-inch mark, followed by the one-eight inch marks. Each of these divisions is labeled on your ruler with a simplified fraction.

To measure using a ruler with fractions, align the left end of the ruler with the edge of the object (directly at the zero inch mark). Then, observe the location of the other edge of the object and where it aligns with the ruler. The mark where the object ends on the ruler is where you will locate its measurement in inches. By understanding the fractional divisions on a ruler, you will be able to make accurate and consistent measurements.

Figure 02 below shows an example of how you could use a ruler with fractions to measure a mini-pencil.

Figure 02: Example of how to use a ruler with fractions to make accurate measurements. (Image: Mashup Math MJ)

Need some extra help with how to measure objects using a ruler? Check out our free video tutorial on YouTube.

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Graphing Inequalities on a Number Line Explained

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Graphing Inequalities on a Number Line Explained

Graphing Inequalities on a Number Line

Math Skills: How to Graph Inequalities on a Number Line

 

Free Step-by-Step Guide: Graphing Inequalities on a Number Line

 

Graphing inequalities on a number line is an important math skill that helps students to visualize all of the possible solutions to any given inequality equation. Whether you are a middle school student learning about inequalities for the first time, or if you simply need a review of how to graph inequalities on a number line, this student guide will teach you everything you need to know about graphing inequalities on a number line.

In this free step-by-step tutorial on Graphing Inequalities on a Number Line, you will learn how to accurately graph an inequality on a number line using a simple three-step method. Once you learn our three-step method for graphing inequalities and work through a few example problems, you will be able to solve any math problem that requires you to graph an inequality on a number line.

This tutorial is organized by the following subtopics (you can follow each section in order or you can use the quick-links below to jump to a subtopic of interest):

Now we are ready to get started with a quick recap of inequalities and what they represent.

 

Lesson Preview: How to Graph Inequalities on a Number Line.

 

Quick Recap: Inequalities

Before we work through some examples of graphing inequalities on a number line, it is important that you understand some key vocabulary and concepts related to inequalities and inequality equations.

What is an inequality?

Definition: In math, an inequality is a relationship where two values or expressions that are not equal to each other are being compared. Since the two values or expressions are not equal, rather than using an equals sign (=), we use an inequality sign.

There are four types of inequalities, each with its own sign:

  • Greater Than: >

  • Less Than: <

  • Greater Than or Equal To: ≥

  • Less Than or Equal To: ≤

These four types of inequality signs are illustrated in Figure 01 below.

 

Figure 01: The four types of inequality symbols.

 

What is an inequality equation?

An inequality equation is an equation that uses an inequality symbol instead of an equals sign.

While an equation with an equals sign has only one possible solution, an inequality equation has infinite possible solutions.

For example, let’s consider the linear equation x=5. The only value of x that would make this equation true is 5 (since 5 is the only number that equals 5).

However, what if we changed the equals to sign (=) to an inequality? For example, consider the inequality x≥5. This inequality means that “x is greater than or equal to 5”. In other words, any value that is equal to 5 or greater would be a solution to this inequality (e.g. 6, 29, 88.3, and 997 would all be solutions).

Again, equations have one possible solution, while inequalities have an infinite amount of possible solutions:

  • Linear Equation: x=5 → 5 is the only solution

  • Inequality: x≥5 → Any value that is 5 or larger can be a solution

Figure 02 below illustrates the difference between the solution of an equation and the solution of an inequality.

 

Figure 02: What is the difference between the solution of a linear equation and the solution of an inequality?

 

Now that you know the difference between the solution of an equation (one possible solution) and the solution of an inequality (infinite amount of solutions), it can be super helpful to graph the solution of an inequality on a number line so that you may visual the set of numbers that holds all of possible solutions of an inequality.

Let’s take a closer look at the graph of the inequality x≥5 on a number line.

This inequality has a solution where x can be any number that is 5 or larger. Here are some examples of solutions and non-solutions:

  • Solutions: 5, 6, 9, 25, 309

  • Non-Solutions: 4, 3, 0, -51

The graph of x≥5 on a number line, as shown in Figure 03 below makes it very easy for us to visualize whether or not a given number is a solution or a non-solution.

 

Figure 03: How to Graph Inequalities on a Number Line: x≥5

 

Looking at the graph above, we can see that there is a shaded circle over 5 and an arrow starting from that circle and moving along the number line towards the right.

Every number beneath this arrow will be a solution to the inequality. Every number that is not underneath the arrow will be a non-solution.

Now that you understand how to read the graph of an inequality on a number line and why such a graph is so useful, you are ready to learn how to graph inequalities on a number line on your own!

How to Graph Solutions to Inequalities on a Number Line

Here are three easy steps that you can follow in reference to graphing inequalities on a number line:

  • Step One: Determine whether the circle will be open or closed and plot it on the number line.

  • Step Two: Make sure that the variable is on the left side of the inequality and determine the direction of the arrow.

  • Step Three: Draw your arrow and complete the graph.

Before we dive into the practice problems, let’s take a closer look at each step.

We will do this by applying the three steps to the inequalities x>7 and x≤6

Step One: Determine whether the circle will be open or closed and plot it on the number line.

For our first step, we have to determine whether or not the circle on our number line over the number 9 will be open or closed.

To make this determination, we have to look at the inequality sign:

  • Open Circle: > or < (means that the number is not included in the solution set)

  • Closed Circle: ≥ or ≤ (means that the number is included in the solution set)

So, we know that:

  • x > 7 will have an open circle on the number line over the number 7

  • x ≤ 6 will have a closed circle on the number line over the number 6

 

Figure 04: Inequalities with a > or < sign will have an open circle and inequalities with a ≥ or ≤ sign will have a closed circle.

 

What is the key difference between an open circle (> or <) and a closed circle (≥ or ≤)?

In cases like x>7 (x is greater than 7), the open circle means that 7 is not a possible solution. This should make sense because 7 is not greater than 7.

In cases like x≤6 (x is less than or equal to 6), the closed circle means that 6 is a possible solution. This should make sense because 6 is less than or equal to 6.

Step Two: Make sure that the variable is on the left side of the inequality and determine the direction of the arrow.

For both of our inequalities, x>7 and x≤6, the variable, x, is already on the left side. So, we just have to determine the direction of the arrow:

  • > or ≥ : arrow travels to the right: →

  • < or ≤: arrow travels to the left: ←

A helpful way to remember how to determine the direction of your arrow is to think of the inequality sign as the head of the arrow. As long as the variable is on the left-side, you can let the direction of the inequality sign dictate the direction of the arrow.

For x>7, the arrow will travel to the right (→), and, for x≤6, the arrow will travel to the left (←).

 

Figure 05: > or ≥ arrow travels to the right: →; < or ≤: arrow travels to the left: ←

 

So, we know that:

  • x > 7 will have an arrow traveling to the right

  • x ≤ 6 will have an arrow traveling to the left

Step Three: Draw your arrow and complete the graph.

For our final step, we simply have to draw our arrow facing in the correct direction and complete our graph.

After completing Step One and Step Two, we determined that:

  • x > 7 has an open circle over 7 with an arrow traveling to the right

  • x ≤ 6 has a closed circle over 6 with an arrow traveling to the left

So, we can complete the graphs of x > 7 and x ≤ 6 as shown in Figure 06 below:

 

Figure 06: The completed graphs of the inequalities x>7 and x≤ 6 on a number line.

 

You have just successfully learned how to graph solutions to inequalities on a number line.

Now that you know the three steps to solving the question, how do I graph an inequality on a number line?, you are ready to take on a few more practice problems.

How to Graph Inequalities on a Number Line

Graphing Inequalities on a Number Line Example 1

Example: Graph the following on a number line: x < 2

For this first example, and all of the examples in this guide, we will use our three-step process to successfully graph the inequality on a number line.

Step One: Determine whether the circle will be open or closed and plot it on the number line (< or > will be open; ≥ or ≤ will be closed).

Let’s start by determining whether our circle will be open or closed. Since the inequality in this example is <, our circle will be open.

  • The graph of the inequality x<2 will have an open circle.

Now we are ready for the next step.

Step Two: Make sure that the variable is on the left side of the inequality and determine the direction of the arrow (> or ≥ : arrow travels to the right: →; < or ≤: arrow travels to the left: ←)

Next, we have to determine the direction of the arrow. Since the variable is already on the left side of the inequality sign, we know that the inequality x<2 will travel to the left (←).

  • The graph of the inequality x<2 will have an arrow that travels to the left (←).

Let’s now move onto the third and final step.

Step Three: Draw your arrow and complete the graph.

Finally, we can draw our graph now that we have already determined that:

  • x < 2 has an open circle over 2 with an arrow traveling to the left

Our completed graph for Example #1 is illustrated in Figure 07 below.

 

Figure 07: Graphing Inequalities on a Number Line: Example #1 Solved

 

Now, let’s move onto our next example of how to graph inequalities on a number line.

How to Graph Solutions to Inequalities on a Number Line Example 2

Example: Graph the following on a number line: x ≥ 0

For this second example, we can again use of three-step process to graph the inequality on a number line.

Step One: Determine whether the circle will be open or closed and plot it on the number line (< or > will be open; ≥ or ≤ will be closed).

In this example, the inequality sign is ≥ (greater than or equal to), so our circle will be closed.

  • The graph of the inequality x ≥ 0 will have a closed circle.

Step Two: Make sure that the variable is on the left side of the inequality and determine the direction of the arrow (> or ≥ : arrow travels to the right: →; < or ≤: arrow travels to the left: ←)

Now we have to figure out which direction our arrow will travel from our closed circle. In this example, the variable is already on the left side of the inequality sign, so we can determine that the arrow for the graph of the inequality x ≥ 0 will travel to the right (→).

  • The graph of the inequality x ≥ 0 will have an arrow that travels to the right (→).

Step Three: Draw your arrow and complete the graph.

Now we have all of the information that we need to graph the inequality on a number line:

  • x ≥ 0 has a closed circle over 0 with an arrow traveling to the right

Figure 08 below illustrates what the completed graph of x ≥ 0 on a number line will look like.

 

Figure 08: How to graph inequalities on a number line: x ≥ 0 has a closed circle over zero on the number line with an arrow traveling from the center of the circle and to the right.

 

Graphing Inequalities on a Number Line Example 3

Example: Graph the following on a number line: -3 < x

We can again use our three-step method to solve our final example, where we have to graph the inequality -3 < x on a number line.

Step One: Determine whether the circle will be open or closed and plot it on the number line (< or > will be open; ≥ or ≤ will be closed).

For the inequality in Example #3, our inequality sign is <, which means that our graph will include an open circle.

  • The graph of the inequality -3 < x will have an open circle.

Now, let’s move onto the second step.

Step Two: Make sure that the variable is on the left side of the inequality and determine the direction of the arrow (> or ≥ : arrow travels to the right: →; < or ≤: arrow travels to the left: ←)

Unlike the first two examples, the inequality in Example #3 has the variable on the right side of the inequality sign: -3 < x

In order to determine the direction of our arrow, we have to “reverse” the order of the inequality equation as follows:

  • -3 < x → x > -3

Notice that, in addition to swapping the position of -3 and x, we also reversed the direction of the inequality sign:

  • < became >

*Whenever you “reverse” the order of an inequality equation to get the variable on the left side like we did in this example, you also have to reverse the direction of the inequality sign.

Now we are left with x > -3, so our variable is on the left side and we can conclude that the arrow for the graph of the inequality on a number line to the right (→).

  • The graph of the inequality x > -3 will have an arrow that travels to the right (→).

Step Three: Draw your arrow and complete the graph.

Finally, we can complete Example #3 by graphing the inequality on a number line using the following information that was collected from Steps One and Two:

  • x > -3 has an open circle over -3 with an arrow traveling to the right

The completed graph of the inequality x > -3 on a number line is shown in Figure 09 below.

 

Figure 09: Graphing Inequalities on a Number Line: x>-3

 

Conclusion: Graphing Inequalities on a Number Line

Unlike linear equations, which have only one possible solution, inequalities have an infinite amount of possible solutions. Graphing inequalities on a number line is a useful way to visualize the infinite amount of values in the solution sets of an inequality.

You can learn how to graph inequalities on a number line by following these three steps:

  • Step One: Determine whether the circle will be open or closed and plot it on the number line (< or > will be open; ≥ or ≤ will be closed).

  • Step Two: Make sure that the variable is on the left side of the inequality and determine the direction of the arrow (> or ≥ : arrow travels to the right: →; < or ≤: arrow travels to the left: ←)

  • Step Three: Draw your arrow and complete the graph.

As long as you can follow these three steps, you can successfully graph inequalities on a number line.

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Free Blank Number Lines for All Grade Levels

Download free PDF number lines for all grade levels and topics.

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How to Convert Percent to Decimal in 2 Easy Steps

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How to Convert Percent to Decimal in 2 Easy Steps

How to Convert Percent to Decimal in 2 Easy Steps

Math Skills: How Do You Convert a Percent to Decimal?

 

Free Step-by-Step Guide: How to Convert Percent to Decimal

 

Every math student must learn and understand how to convert percent to decimal. This simple math skill has tons of practical applications both inside the classroom and in real life as well.

In this free guide to How to Convert Percent to Decimal, you will learn an easy two-step method for converting any percent into a decimal. Once you learn how to apply the two-steps, you will be able to quickly and accurately turn percents to decimals. The guide covers the following subtopics, and you can use the quick-links below to jump to a section of interest if you wish:

Once you work through the examples in this guide, you will have a strong understanding of how to turn percent to decimal in a variety of cases.

Are you ready to get started?

 

Lesson Preview: How to Convert Percent to Decimal Explained

 

How to Convert Percent to Decimal

We will begin this guide to converting percents into decimals by reviewing a few important vocabulary terms in reference to percentages and decimals.

Definition: In math, a percentage (or a percent) is a value or number that can be expressed as a fraction with where the denominator is 100. For example, 25% is equivalent to the fraction 25/100.

Definition: In math, a decimal is a value that represents a whole number with a fractional part. The fractional part will always have a denominator that is equal to 10 or a multiple of 10. For example, the decimal 0.8 is equal to the fraction 8/10.

Percents and decimals have a proportional relationship and they both can be used to represent a value. Whether you choose to express values as percents or as decimals often depends on the situation. Sometimes, it makes more sense to represent values as percents, and other times it is more useful to express values in decimal form. Given this relationship between percents and decimals, it is incredibly useful for you to be able to quickly and accurately convert between the two, especially converting a percent to decimal.

 

Figure 01: How to Convert Percent to Decimal: 85% converted to a decimal is 0.85

 

How to Convert Percent to Decimal in 2 Steps

Now that we have reviewed the key vocabulary terms and relationships related to percents and decimals, we are ready to learn how to turn percent to decimal by following two simple steps:

  • Step One: Rewrite the percent without the % symbol

  • Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

If you can learn how to apply these two simple step s, you will be able to successfully convert any percent into a decimal number.

For example, let’s apply these two steps to converting 85% into a decimal number.

Step One: Rewrite the percent without the % symbol

For the first step, we simply have to take the percentage value and rewrite it without the % symbol as follows:

  • 85% → 85

Now we can move onto Step Two.

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

For the second step, we have to see if the result from Step One has a decimal point. If it doesn’t already have one, we have to add one. Then, we just have to take that decimal point and shift it two units to the left as follows:

  • 85 → 85.0

  • 85.0 → .85 → 0.85

Final Answer: 85% = 0.85

That’s all that there is to it!

 

Figure 02: You can convert a percent to decimal by shifting the decimal place two places to the left.

 

Ready to gain some more experience with using our two-step method for how to turn percent to decimal? Let’s move onto the next section where we will work through five different examples.

How Do You Convert a Percent to Decimal?

Convert Percent to Decimal Example #1

Example: Convert 40% to a decimal.

For Example #1, we have to convert 40% to a decimal number. We can solve this problem by following our two-step method as follows:

Step One: Rewrite the percent without the % symbol

We can complete Step One by rewriting 40% without a percentage symbol as follows:

  • 40% → 40

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

Since our result from Step One, 40, doesn’t have a decimal point, we have to add one and then move it two places to the left as follows:

  • 40 → 40.0

  • 40.0 → .4 → 0.4

Final Answer: 40% = 0.4

We have now solved the first example and we can say that 40% is equal to 0.4.

Figure 03 below illustrates how we used our two-step method to solve this first problem.

 

Figure 03: How to Convert Percent to Decimal: 40% = 0.4

 

Are you ready to try another example?

Convert Percent to Decimal Example #2

Example: Convert 79% to a decimal.

For this next example, we can again use our two-step method for converting percents to decimals as follows:

Step One: Rewrite the percent without the % symbol

Just like the last example, we start off by rewriting the percent value without the % symbol as follows:

  • 79% → 79

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

Since 79 does not have a decimal point, we have to add one and then shift it to the left two places.

  • 79 → 79.0

  • 79.0 → .79 → 0.79

Final Answer: 79% = 0.79

So, we can conclude that 79% is equal to 0.79.

Figure 04 displays how we solved Example #2.

 

Figure 04: How do you convert a percent to decimal?

 

Convert Percent to Decimal Example #3

Example: Convert 3% to a decimal.

Are you starting to get the hang of it? Let’s move onto to this third example, where we have to convert 3% into a decimal value.

Step One: Rewrite the percent without the % symbol

Start off by rewriting 3% without the percentage symbol:

  • 3% → 3

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

 
3% = 0.03

3%=0.03

 

Next, we have to add a decimal point and then shift it two places to the left as follows:

  • 3 → 3.0

  • 3.0 → .03 → 0.03

Final Answer: 3% = 0.03

Finally, we can conclude that 3% is equal to 0.03.

The entire step-by-step process for converting this percent to decimal is shown in Figure 05 below.

 

Figure 05: How to Turn Percent to Decimal: 3% = 0.03

 

Convert Percent to Decimal Example #4

Example: Convert 6.2% to a decimal.

For this fourth example, we are dealing with a percentage that includes a decimal. Luckily, we can still use our two-step method to convert to percent to a decimal.

Step One: Rewrite the percent without the % symbol

Just like the previous examples, our first step is to rewrite the percent without the % sign.

  • 6.2% → 6.2

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

 

6% = 0.062

 

In this case, we don’t have to add a decimal because there already is one (between 6 and 2 in 6.2). So, we just have to take that decimal point and shift it two places to the left as follows:

  • 6.2 → .062 → 0.062

Final Answer: 6.2% = 0.062

The entire step-by-step process for converting this percent to decimal is shown in Figure 06 below.

 

Figure 06: How to Convert Percent to Decimal Example #4

 

Convert Percent to Decimal Example #5

Example: Convert 115% to a decimal.

For our fifth and final example, we have to convert a percent that is great than 100% into a decimal. Even in situations like, we can still use our two-step method to accurately convert the percent to decimal.

Step One: Rewrite the percent without the % symbol

Just like all of the previous examples, we start out by rewriting 115% without the percent symbol as follows:

  • 115% → 115

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

 

115% = 1.15

 

To complete Step Two, we just have to add a decimal point at the end 115 and then shift it two places to the left as follows:

  • 115 → 115.0

  • 115.0 → 1.150 → 1.15

Note that we don’t have to include the zero at the end of 1.150 and we can conclude that:

Final Answer: 115% = 1.15

All of the steps that were followed to complete this last example are shown in Figure 07 below.

 

Figure 07: How to convert percent to decimal when the percent is greater than 100.

 

Conclusion: How to Convert Percent to Decimal

Being able to quickly and accurately convert a percent to a decimal is an important and useful math skill that every student must master.

You can successfully convert any percent into a decimal by following two simple steps:

  • Step One: Rewrite the percent without the % symbol

  • Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

In this guide on how to turn percent to decimal, we worked through five step-by-step examples where we made the following conversions:

  • 40% = 0.4

  • 79% = 0.79

  • 3% = 0.03

  • 6.2% = 0.062

  • 115% = 1.15

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How to Convert Decimal to Percent in 2 Easy Steps

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How to Convert Decimal to Percent in 2 Easy Steps

How to Convert Decimal to Percent in 2 Easy Steps

Math Skills: How Do You Convert a Decimal to Percent?

 

Learn how to convert decimal to percent.

 

Understanding how to convert decimal to percent is an important and useful math skill with applications inside the classroom and in the real world.

This free Step-by-Step Guide on How to Convert Decimal to Percent will teach you a simple 2-step method to converting a decimal to a percent whenever you are solving math problems are dealing with real-world scenarios involving decimals and percents. This free guide is organized based on the following topics:

You can work through each section in sequential order, or you can click on any of the text links above to jump to any particular section of this guide.

Are you ready to learn how to convert decimal to percent? Let’s get started!

 

Lesson Preview: How to Convert Decimal to Percent in Two Steps.

 

How to Convert a Decimal to a Percent

Before we learn the step-by-step process for how to convert a decimal to a percent, it’s important that you understand some key vocabulary and concepts related to decimals and percents.

Definition: In math, a decimal is a way of expressing a whole number that has a fractional part (where the fractional part is always out of 10 or a multiple of 10). These types of numbers include a whole number and a fractional part that are separated by a decimal point.

Definition: In math, a percent is a number that can be expressed as a fraction with a denominator of 100.

Whenever you are converting a decimal to a percent, you are essentially converting a fraction with a denominator of 10 (or a multiple of 10) to a fraction with a denominator of 100.

It is important to note that decimals and percents are two different ways to express the same value. In some cases, it will be more useful to work with numbers as decimals. And, in other cases, it will be more useful to work with numbers as percents. Knowing how to easily convert a decimal to percent will allow you to be successful in both types of situations.

 

Figure 01: The decimal 0.75 converted to a percent is 75%. Both values represent 75/100.

 

How to Convert a Decimal to a Percent in 2 Steps

Now that you are familiar with the relationship between a decimal and a percent, you are ready to learn our easy 2-step method for how to convert a decimal to percent.

  • Step One: Multiply the Decimal Value by 100

  • Step Two: Write the Result as a Percentage.

As long as you can follow these two steps, you can easily convert a decimal to a percent.

For example, let’s use our two-step method to convert the decimal 0.75 to a percent.

Step One: Multiply the Decimal Value by 100

Our first step is to take the decimal 0.75 and multiply it by 100 as follows:

  • 0.75 x 100 = 75

Note that multiplying a decimal by 100 is the same as taking the decimal point and moving it two places to the right. In this case, multiplying 0.75 results in 75.0, or just 75.

Step Two: Write the Result as a Percentage.

The next step is to take your result from Step One and express it as a percentage as follows:

  • 75 → 75%

Final Answer: 0.75 = 75%

Note that you can express your final answer as 75% or 75.0% (either one is correct).

 

Figure 02: You can convert a decimal to a percent by multiplying the decimal by 100 (or simply by shifting the decimal point two places to the right).

 

Now that you know how to convert a decimal to percent using our 2-step method, let’s gain some more practice and experience making conversions by working through a few more practice problems.

How Do You Convert a Decimal to Percent?

Convert Decimal to Percent Example #1

Example: Convert 0.5 to a percent.

For this first example, we want to convert the decimal 0.5 to a percent. We can make this conversion by following our 2-step method as follows:

Step One: Multiply the Decimal Value by 100

For Step One, we have to multiply the decimal value 0.5 by 100 as follows:

  • 0.5 x 100 = 50

Again, if you are unsure of how to multiply a decimal by 100, you can find the answer simply by shifting the decimal point two places to the right.

Step Two: Write the Result as a Percentage.

Finally, we have to take our result from Step One and express it as a percent (i.e. express the value from Step One with a percentage sign attached to it) as follows:

  • 50 → 50%

Final Answer: 0.50 = 50%

So, we can say that the decimal 0.50 is equal to 50%.

The step-by-step process for solving this first example is illustrated in Figure 03 below.

 

Figure 03: How to Convert Decimal to Percent.

 

Now, let’s move onto the next example.

Convert Decimal to Percent Example #2

Example: Convert 0.36 to a percent.

Let’s go ahead and use our two-step method to solve this next example.

Step One: Multiply the Decimal Value by 100

Just like we did in the last example, our first step to converting a decimal to percent is to multiply the percent by 100:

  • 0.36 x 100 = 36

Remember that multiplying a decimal by 100 is the same thing as moving the decimal point two places to the right.

Step Two: Write the Result as a Percentage.

For the second step, we have to express our result from Step One as a percentage:

  • 36 → 36%

Final Answer: 0.36 = 36%

Are you starting the get the hang of it? Figure 04 below shows how we used our two-step method to solve Example #2.

 

Figure 04: How Do You Convert a Decimal to Percent?

 

Convert Decimal to Percent Example #3

Example: Convert 0.08 to a percent.

For this third example, we can again use our 2-step method to make this conversion:

Step One: Multiply the Decimal Value by 100

First, multiply the decimal by 100:

  • 0.08 x 100 = 8

You could have also just moved the decimal point to places to the right as follows:

  • 0.08 → 8.0 or 8

Step Two: Write the Result as a Percentage.

Next, we just have to express our result from Step One as a percentage:

  • 8 → 8%

Final Answer: 0.08 = 8%

Figure 05 below illustrates how we solved Example #3.

 

Figure 05: Decimal to Percent: 0.08 = 8%

 

Convert Decimal to Percent Example #4

Example: Convert 0.045 to a percent.

Let’s continue using our two-step method to solve this problem:

Step One: Multiply the Decimal Value by 100

Start off by multiplying the decimal by 100:

  • 0.045 x 100 = 4.5

Note that you would end up with the same result (4.5) if you had just moved the decimal point two places to the right:

  • 0.045 → 4.5

Step Two: Write the Result as a Percentage.

Finally, we can express the result from Step One as a percent as follows:

  • 4.5 → 4.5%

Final Answer: 0.045 = 4.5%

 

Figure 06: Convert a Decimal to Percent: 0.045 = 4.5%

 

Convert Decimal to Percent Example #5

Example: Convert 1.39 to a percent.

We can use our two-step method for how to convert decimal to percent to solve this final example:

Step One: Multiply the Decimal Value by 100

The first step is to multiply the decimal by 100 as follows:

  • 1.39 x 100 = 139

Step Two: Write the Result as a Percentage.

Next, express the answer from the first step as follows:

  • 139 → 139%

Final Answer: 1.39 = 139%

 

Figure 07: Decimal to Percent Conversion: Example #5

 

Conclusion: How to Convert Decimal to Percent

Knowing how to quickly convert decimal to percent is a useful and important math skill with many academic and real-world applications.

You can easily convert a decimal to a percent by using a simple two-step method:

  • Step One: Multiply the Decimal Value by 100

    Multiplying a decimal by 100 is the same as moving the decimal point two places to the right.

  • Step Two: Write the Result as a Percentage.

In this step-by-step guide, we used this two-step method to make the following conversions from decimal to percent:

  • 0.5 = 50%

  • 0.36 = 36%

  • 0.08 = 8%

  • 0.045 = 4.5%

  • 1.39 = 139%

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How to Find Median in 3 Easy Steps

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How to Find Median in 3 Easy Steps

How to Find Median in Math Step-by-Step

Math Skills: How to find the median of a data set in 3 easy steps

 

Are you ready to learn how to find the median of a data set?

 

Finding the median of a data set is an important skill that will help you to analyze and make conclusions about data.

In math, the word median means middle and it refers to the middle number in a data set where the values are organized from smallest to largest.

In this Free Step-by-Step Guide on How to Find Median, you will learn how to find the median of a data set using a simple 3-step method, which we will practice and apply to several example problems. This guide will cover the following sections/topics:

You can click on any of the quick-links above to jump to any topic/section of this guide, or you can follow each section in order (we highly recommend this option if you are new to this topic).

Let’s begin!

 

Lesson Preview: How to find median in math in 3 easy steps.

 

What is the Median of a Data Set?

In statistics, a data set is a group of numbers that represent some form of data.

For example, consider a data set that represents the ages of 5 different students:

  • 12, 13, 15, 17, and 20

Note that a values in a data set can be represented as a list of numbers (as shown above) or contained with a set of curly brackets as shown below:

  • {12, 13, 15, 17, 20}

Note that both of these options represent the same data set, which, in this case, represents the ages of students.

Figure 01 below illustrates this data set and what the values represent.

 

Figure 01: This data set represents the ages of five different students.

 

In math, the median of a data set is the middle value of a set of data that is arranged in order from smallest to largest from left to right.

As long as the values in a data set are arranged in order of smallest to largest, you can simply locate the middle value to determine the median of the data set.

You can find the median, or middle, value of any data set by following these three simple steps:

  • Step One: List all of the numbers in order from smallest to largest

  • Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

  • Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

Before we move onto any example problems of how to find the median of a data set, let’s apply these three steps to finding the median of the previously mentioned data set that represented the ages of five students as 12, 13, 15, 17, and 20.

Step One: List all of the numbers in order from smallest to largest

If we wanted to find the median of the data set that represented student’s ages, we would first have to make sure that the values are indeed in order from smallest to largest:

  • 12, 13, 15, 17, 20

It is easy to see that the numbers in the data set are arranged in order from smallest to largest.

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

  • 12, 13, 15, 17, 20

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

In this case, the middle number is 15, so we can skip the third step and conclude that:

Final Answer: The median is 15.

Note that, later on in this guide, we will work through example problems where Step Three will be necessary.

The 3-step process for how to find median is displayed in Figure 02 below.

 

Figure 02: The median of a data set with values arranged in order from smallest to largest is the middle value.

 

Now that you are familiar with the concept of a median of a data set and what it represents, you are ready to gain some more practice with how to find median using our 3-step method.

How to Find Median Examples

How to Find the Median of a Data Set Example #1

Example: Find the Median of the Data Set:

Data Set: 3, 9, 11, 5, 17, 8, 16

Step One: List all of the numbers in order from smallest to largest

Notice that the numbers in our data set are not in order from smallest to largest. We can rewrite the data set so that the numbers are indeed in order as follows:

  • 3, 5, 8, 9, 11, 16, 17

Now that the numbers in our data set are arranged in order from smallest to largest, we are ready for our second step.

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

Since our data set has an odd number of values, we pinpoint one exact middle term, which, in this case, is 9:

  • 3, 5, 8, 9, 11, 16, 17

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

In cases such as this, we can skip our third step and conclude that:

Final Answer: The median is 9.

Figure 03 below illustrates how we solved this first example step-by-step.

 

Figure 03: How to Find Mean Using 3 Easy Steps.

 

Notice that our data set for this first example has an odd amount of values (the data set had 7 total values). Whenever this is the case, you will be able to identify one single number and skip Step Three.

However, whenever there is an even amount of values, there will be two middle numbers and you will have to perform the third step to determine the median, which will be the case in the next example.

How to Find the Median of a Data Set Example #2

Example: Find the Median of the Data Set:

Data Set: 5, 14, 4, 9, 24, 16, 10, 18

Step One: List all of the numbers in order from smallest to largest

Our first step is to arrange all of the numbers in order from smallest to largest as follows:

  • 4, 5, 9, 10, 14, 16, 18, 24

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

Unlike the last example which had a data set with an odd amount of numbers, the data set in this example has an even amount of numbers (there are 8 total values).

In cases like this, when there is an even amount of numbers in the data set, there will be two middle numbers:

  • 4, 5, 9, 10, 14, 16, 18, 24

Notice that both 10 and 14 are both in the middle. Whenever there are two middle numbers, you will have to complete Step Three to determine the median of the data set.

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

To find the median of a data set with two middle numbers, you simply have to find the average of the two numbers. You can do this by adding the two middle numbers together and then dividing by two as follows:

  • 10 + 14 = 24

  • 24 ÷ 2 = 12

Final Answer: The median is 12.

The step-by-step process for how to find a median of a data set with an even amount of values is shown in Figure 04 below.

 

Figure 04: How to Find Median of a Data Set with Two Middle Numbers.

 

Now that you are familiar with how to find median when a given data set has an odd amount of numbers or an even amount of numbers, let’s work through two more examples to further reinforce your understanding of how to find a median.

How to Find the Median of a Data Set Example #3

Example: Find the Median of the Data Set:

Data Set: 2, 58, 40, 17, 15, 16, 31, 6, 10, 18, 67, 23, 96

Step One: List all of the numbers in order from smallest to largest

First, rewrite the numbers as a list in order from smallest to largest:

  • 2, 6, 10, 15, 16, 17, 18, 23, 31, 40, 58, 67, 96

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

Notice that this particular data set has an odd amount of numbers (there are 13 total values). So, we can determine the middle value on the second step:

  • 2, 6, 10, 15, 16, 17, 18, 23, 31, 40, 58, 67, 96

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

Since this data set had an odd amount of values, we were able to identify the median in Step Two and we can conclude that:

Final Answer: The median is 18.

Figure 05 below shows how we identified the median in Example #3.

 

Figure 05: How to Find a Median of a Data Set.

 

How to Find the Median of a Data Set Example #4

Example: Find the Median of the Data Set:

Data Set: 2, 9, 5, 8, 4, 10, 3, 15, 1, 25

Step One: List all of the numbers in order from smallest to largest

Just like the previous examples, we begin by rearranging the numbers in the data set so that they are in order from largest to smallest:

  • 1, 2, 3, 4, 5, 8, 9, 10, 15, 25

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

The data set in this Example #4 has an even amount of numbers (there are 10 total values).

Whenever there is an even amount of numbers in the data set, there will be two middle numbers:

  • 1, 2, 3, 4, 5, 8, 9, 10, 15, 25

Both 5 and 8 are in the middle, so we have to move onto Step Three to determine the value of the median.

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

We can identify the median by finding the average of the two middle numbers as follows:

  • 5 + 8 = 13

  • 13 ÷ 2 = 6.5

Final Answer: The median is 6.5.

Notice that our final answer is a decimal, which is totally fine and quite common!

 

Figure 06: How to Find a Median Step-by-Step

 

Conclusion: How to Find Mean

Knowing how to find the median of a data set is an important and useful math skill that every student must learn.

The median of a data set that is arranged in order from smallest to largest is the middle value (i.e. median = middle).

You can find a median by applying the following three-step method:

  • Step One: List all of the numbers in order from smallest to largest

  • Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

  • Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

Note that, for data sets with an odd amount of values, Step Three can be skipped. However, whenever a data set has an even amount of values, there will be two middle numbers and following Step Three will be necessary for finding the median value.

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