Explore Decimals

# Decimals to Improper fractions

Decimals are super useful, but sometimes they’re just not what we need in a given scenario.

The good news is that you can convert your decimals into fractions — even improper fractions! We know that an improper fraction has a numerator greater than the denominator, so any decimal with the whole part greater than $$0$$ can be rewritten as an improper fraction.

Let’s see how!

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

Converting a decimal to an improper fraction just means rewriting the decimal as an improper fraction. If the whole part of your decimal number is greater than zero, we can write it as an improper fraction! And just like converting decimals to fractions in general, our denominator will be a multiple of $$10$$.

All we need to do is write the number without the decimal point and divide it by a multiple of $$10$$, depending on how many places are used after the decimal point.

For example, the decimal $$3.5$$ can be written as $$\frac{35}{10}$$, which when simplified turns out to be $$\frac{7}{2}$$. Sweet!

### Why is rewriting decimals as improper fractions useful?

As you may already know, sometimes it can be hard to calculate with the decimals, like when the fractional parts of the decimals are periodic. A great example of that is the decimal $$1.\overline{3}$$, which can be rewritten as the improper fraction $$\frac{4}{3}$$.

Okay, let’s do some math!

## How to rewrite decimals as improper fractions

We mentioned a few examples above, but let’s really dive into the details of a few together. Ready?

### Example 1

Rewrite the decimal number as an improper fraction:

$${1}{.}25$$

First, we’ll write all the numbers above a fraction line, leaving out the decimal sign:

$$\frac{125}{}$$

Our original number has two decimal places after the decimal sign, so our denominator will be a multiple of $$10$$ with two zeroes:

$$\frac{125}{100}$$

All that’s left to do is simplify! We can see our fraction can be reduced by $$25$$, so let’s divide the numerator and the denominator by $$25$$:

$$\frac{125\div25}{100\div25}$$

Finish your calculations, and drum roll

$$\frac{5}{4}$$

There it is! We turned our decimal into an improper fraction.

### Example 2

Rewrite the decimal as a fraction:

$$2.582$$

Our first step is to write all the numbers above a fraction line, leaving out the decimal sign:

$$\frac{2582}{}$$

The original decimal number has three places after the decimal point. That means the denominator will be the multiple of $$10$$ with three zeroes:

$$\frac{2582}{1000}$$

Now let’s write the fraction in its simplest form! This fraction can be reduced by $$2$$, so we’ll divide the numerator and the denominator by $$2$$:

$$\frac{2582\div2}{1000\div2}$$

Divide the numbers in the numerator and denominator to get:

$$\frac{1291}{500}$$

We did it again! Another beautiful improper fraction.

That wasn’t too bad, right? Now that we’ve walked through some examples, let’s review the process so you can use it on any problem:

## Study summary

1. Put all numbers in the numerator, leaving out the decimal point.
2. Use the number of decimal places to determine the multiple of 10 that should be in the denominator.
3. If possible, simplify the improper fraction.

## Do it yourself!

We think you’re getting the hang of it! Prove it by solving these practice problems:

Rewrite the decimal as a fraction:

1. $$1.3$$
2. $$5.33$$
3. $$2.592$$
4. $$7.672$$

Solutions:

1. $$\frac{13}{10}$$
2. $$\frac{533}{100}$$
3. $$\frac{324}{125}$$
4. $$\frac{959}{125}$$

If you’re struggling, that’s totally okay! Stumbling a few times is actually good for learning. If you get too stuck, scan the problem using your Photomath app, and we’ll walk you through to the other side!

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

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## Got arithmetic homework?

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