Dividing Decimals: How to Turn a Decimal Into A Fraction

Three blind mice. Three blind mice.

See how they run. See how they run.

The Farmer’s Wife went after them with a carving knife

And divided them up for stew that night.

Filling eleven pots of rice.

Okay, that might not be the loveliest example of dividing decimals and converting into fractions and vice versa, but turning decimals into fractions is a useful skill to have. Plus, it’s super easy!

turn a decimal into a fraction

Dividing Decimals Example # 1.

Let’s take any decimal: 0.65

We know that 0.65 is more than half (0.5) but less than three quarters (0.75). But what is the exact fraction?

Let’s place the number over 1 in a fraction:
0.65/1

Then, count the number of digits in the decimal. We have 2 That means we must multiply it by that many place holders.

So we multiply both sides by 100
(0.65/1) X (100/100)

This gives you your fraction!
65/100

From there, we can reduce it to the simplest number possible:
13/20

Your answer is 13/20

Dividing Decimals Example # 2.

Let’s take a more complex number:

0.525

Set it up:

(0.525/1) X (1000/1000) = 525/1000

Then simplify it!

(525/1000) ÷ (5/5) = (105/200) ÷ (5/5) = 21/40

Your answer is 21/40

Dividing Decimals Example # 3.

Let’s take a very complex number:

0.54587123658654

Don’t be intimidated. This is a piece of cake!

0.54587123658654/1

Count the number of digits: 14

Multiply it by that number of place holders:

100000000000000/100000000000000

Then reduce the number by dividing both sides by 2…

54587123658654/100000000000000 = 27293561829327/50000000000000

27293561829327/50000000000000 is the answer!

Dividing Decimals Example # 4.

What if you have a mixed number?  Like, 5.623?

First, ignore the whole number. Set 5 aside.

Then, work with the decimal. 0.623

You can do it! Remember to count the number of digits after the decimal?

(623/1) X (1000/1000) = 623/1000

dividing decimals

Let’s go back to the Farmer’s Wife.

She had 3 mice and eleven cups of stew

3 ÷ 11 = 0.273

What is the fraction of mouse per stew?

273/1000

The number can’t be reduced further. This is the fraction of mouse per cup of stew!

Time for lunch!

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