What is .875 as a fraction?

When dealing with numbers, it is common to see them in both fraction and decimal form. And while a value in decimal form may look very different from its fractional form, they both represent the exact same value. In math, it is incredibly important to be able to understand the relationship between a value in fraction form and decimal form and, more importantly, how to convert a decimal to a fraction and vice versa. This quick guide will focus on the decimal 0.875 as a fraction.

Answer: .875 as a fraction equals 7/8

(The answer above is in simplest form)

Next, we will explore why 0.875 as a fraction is equivalent to 7/8

Why does 0.875 as a fraction equal 7/8? How to Make the Conversion:

The first step to converting .875 from a decimal to a fraction is to figure out the place value of the final digit of the decimal 0.875 (i.e. the digit farthest to the right of the decimal point). In the case of 0.875, the digit that is farthest to the right of the decimal point is 5, which is in the thousandths (1/1,000) place value slot.

If correctly identifying this place value is confusing to you, it can be extremely helpful to use a place value chart as a visual aide as shown below:

Learn how convert any decimal into fraction in 3 easy steps? Click here to access our free guide How to Convert a Decimal to a Fraction

Now, the next step is to write .875 as a fraction with a denominator of one as follows:

0.875/1

From here, the next task is to multiply both the numerator and the denominator of the fraction by the place value of the last digit, which was the thousandths decimal place in this case. Therefore, you would multiply the top of the fraction by 1,000 and the bottom of the fraction by 100 as follows:

(0.875 x 1,000) / (1 x 1,00) = 875/1000

At this point, you can say that the 0.875 as a fraction is equal to 875/1000

But can this fraction be reduced?

The fraction 875/1000 can be reduced down to 3/8. Here’s how:

To rewrite the fraction 875/1000 in reduced form, you must find the Greatest Common Factor (GCF) between the numerator value 875 and the denominator value 1,000. (Note: In math, a factor is any value that can be divided equally into another number without any remainder).

So, lets list all of the factors of 875 and 1,000 so that we may identify the GCF:

Factors of 875: 1, 5, 7, 25, 35, 125, 175, 875
Factors of 1,000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

Using our list, you should notice that GCF of 875 and 1,000 is: 125

Finally, take the GCF of 125 and divide it into both the numerator and the denominator of 875/1000 as follows:

(875 ÷ 125) / (1,000÷ 125) = 7/8