Explore Decimals

# Decimals to fractions

Decimals are cool and all, but sometimes it just makes more sense to work with fractions. Wouldn’t it be nice if we could convert decimals into fractions?

Good news: We can!

Let’s learn how.

## What does it mean to convert a decimal to a fraction?

Converting a decimal to a fraction just means writing the decimal as a fraction. It’s pretty simple, too!

Any decimal number can be written as a fraction with a denominator of a multiple of $$10$$. Basically, you just write the number without the decimal point and divide it by a multiple of $$10$$, depending on the number of places after the decimal point.

For example, the decimal $$0.5$$ can be written as $$\frac{5}{10}$$, which, when simplified, turns out to be $$\frac{1}{2}$$.

Think of it this way: that $$5$$ is in the tenths place, so you could read it as “point five,” but really it’s “five tenths.” Hey, that’s a fraction!

Cool, right?

### Why is converting decimals into fractions so useful?

We love decimals, but sometimes they’re just not the vibe. For instance, let’s say you found a milkshake recipe online, and it says you need $$0.75$$ cups of milk. But — oh no! — your measuring cup has fractions on it, not decimals. You can rewrite $$0.75$$ as $$\frac{75}{100}$$ and then simplify to realize you need to fill your measuring cup to the $$\frac{3}{4}$$ mark.

Phew! Milkshake crisis averted.

## How to convert a decimal to a fraction

Ready to see how it’s done? Let’s walk through some examples together.

### Example 1

Rewrite the decimal as a fraction:

$$0.25$$

First, we’ll draw our fraction bar and use the piece after our decimal as the numerator:

$$\frac{25}{}$$

In this example, we have two decimal places after the decimal point. That means we’ll use the multiple of $$10$$ with two zeroes as the denominator — a.k.a. $$100$$:

$$\frac{25}{100}$$

Now all we have to do is simplify! This fraction can be reduced by $$25$$, so let’s divide the numerator and the denominator by $$25$$:

$$\frac{25\div25}{100\div25}$$

Divide the numbers in the numerator and denominator:

$$\frac{1}{4}$$

Now we have our fraction in its simplest form! Shall we try another?

### Example 2

Rewrite the decimal as a fraction:

$$0.582$$

Our first step is to draw our fraction bar and use the portion after our decimal point as the numerator:

$$\frac{582}{}$$

There are three decimal places after the decimal point, so our denominator will be the multiple of $$10$$ with three zeroes:

$$\frac{582}{1000}$$

Now let’s simplify! Notice that the fraction can be reduced by $$2$$, so let’s divide the numerator and denominator by $$2$$:

$$\frac{582\div2}{1000\div2}$$

Finish your calculations in the numerator and denominator:

$$\frac{291}{500}$$

Ta-da!

That wasn’t so bad, right? Let’s review the steps so that you can apply them to any example:

## Study summary

1. Place the numbers after the decimal point above a fraction bar (instant numerator!)
2. Use the number of decimal places to determine which multiple of 10 will end up as the denominator.
3. If possible, simplify the fraction.

## Do it yourself!

You might not think practicing math is the most glamorous way to spend your time, but the repetition really helps cement the method in your mind. So, when you’re ready, we’ve got some practice problems for you!

Rewrite the decimal as a fraction:

1. $$0.222$$
2. $$0.358$$
3. $$0.001$$
4. $$0.95$$

Solutions:

1. $$\frac{111}{500}$$
2. $$\frac{179}{500}$$
3. $$\frac{1}{1000}$$
4. $$\frac{19}{20}$$

If you’re having some trouble, don’t worry! You can scan the problem using your Photomath app and we’ll walk you through each step in as much detail as you need.

Here’s a sneak peek of what you’ll see:

/

## Got arithmetic homework?

Head over to the Photomath app for instant, step-by-step solutions to all of your arithmetic problems.