# How do you convert 87.5% as a fraction and a decimal?

Nov 17, 2014

There is a very simple trick to converting percentages to decimals and fractions.

When you are given a %, like 87.5%, all you have to do is move the decimal point over to the left two spaces to get the decimal form of it. So, 87.5% is converting into $.875$.

To change a % into a decimal, think about 87.5% like a grade on a test. Tests are usually out of 100 point, and scoring an 87.5% on one means you got $87.5$ points out of $100$.

So, converting that into a fraction, you get:

$\frac{87.5}{100}$

And since you don't want decimals in your fractions, you can change that to:

$\frac{875}{1000}$

Now, simply reduce the fraction by dividing both the numerator and the denominator by 5:

$\frac{875 \div 5}{1000 \div 5}$ = $\frac{175}{200}$

$\frac{175 \div 5}{200 \div 5}$ = $\frac{35}{40}$

$\frac{35 \div 5}{40 \div 5}$ = $\frac{7}{8}$

Hope that helped!

Jun 20, 2016

Fraction = $\frac{7}{8}$

Decimal = $0.875$

#### Explanation:

The answer that has already been given is perfect in and by itself. I just want to give you some methods for doing these type of questions so that you won't stagger when you see these type of questions in exams (like the SAT).

Whenever you see such questions, remember the following things. These are conversions of English words to Mathematical tools.

What $=$ Any variable like $x$

Percent / Percentage / % $=$ Divide by 100

of $=$ Multiply

is $=$ Put an equal to ($=$) sign

I'll give you an example through a question.

What percent of 200 is 5?

Ans: Replace English words by mathematical tools according to the rules I told you.

$x$( What) /100 ( percent) $\times$( of) 200 $=$( is) 5

In a refined form, $\frac{x}{100} \times 200 = 5$

Calculate x. On calculating, x comes out to be $2.5$

So, 2.5 percent of 200 is 5.

Now your question is actually very simple if you follow my rules.

You want 87.5%. By the rules, % means divided by 100. So

87.5% = 87.5/100 and now using the same strategy, Ans: $\frac{875}{1000}$

Disregard the next section if you know how to convert a decimal to a fraction

Section Starts

First, I'll write the decimal form. Whenever you divide by a number that is in form of 1 followed by $n$ number of zeroes. (here 1 is followed by 2 zeroes), you should shift the decimal point to the left side by n places.

In this case, shift decimal point in 87.5 to the left by 2 places. So this becomes 0.875.

This is the answer in decimal point.

Now simultaneously, I'll teach you how to convert a decimal into a fraction.

Here, you see 2 types of "numbers". One to the left side of the decimal point and one to the right side of the decimal point.

Here, left side of decimal point is 0 and right side of decimal point is 875.

Count the number of digits in the number to the right side of the decimal point (Here, the number of digits is 3)

Remove the decimal point and divide the number by a number formed by 1 followed by the "digits" we obtained (i.e. 3).