Explore Fractions

# Fractions to decimals

Fractions: We know and love them, but sometimes it’s easier to work with decimals, depending on our situation. It sure would be great if we could turn fractions into decimals… well, actually, we can!

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

Converting a fraction to a decimal just means that we’re writing a fraction in decimal notation. It’s actually a pretty simple process, too!

You just have to divide the numerator of the fraction by its denominator. For example, the fraction $$\frac{1}{2}$$ written as a decimal is $$0.5$$.

Doesn’t it look like a fraction with little decimal points as its numerator and denominator? Hopefully with that visual, you’ll remember that dividing a fraction gets you a decimal!

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

Let’s say we’ve got a fraction in front of us, and we need to figure out which integer is closest on a number line, or we need to round a number. Something like this is so much easier when we use decimals! Luckily, we have the option to convert our fractions into decimals whenever we need.

## How to convert a fraction to a decimal

Now that we’ve got all that covered, let’s see how we actually convert a fraction into a decimal number! Here are a few examples we can work through together:

### Example 1

Rewrite the fraction as a decimal:

$$\frac15$$

To rewrite our fraction as a decimal, we simply divide the numerator by the denominator:

$${1}\div5$$

Divide $$1$$ by $$5$$ and write the remainder:

$${1}\div{5}=0$$

$$\text{remainder}=1$$

We used all our digits, so to continue dividing, let’s write the decimal sign in the quotient and add a $$0$$ to the remainder:

$$1\div5=0.$$

$$\text{remainder}=10$$

Now divide the remainder $$10$$ by $$5$$, then write the result after the decimal sign. Do we have another remainder?

$$1\div5=0.2$$

$$\text{remainder}=0$$

In this case, the remainder is now $$0$$, so we’re done! Our result is:

$$1\div5=0.2$$

Great work! Let’s kick it up a notch, shall we?

### Example 2

Rewrite the fraction as a decimal:

$$\frac{147}{250}$$

To rewrite the fraction as a decimal, we’ll just divide the numerator by the denominator:

$${147}\div250$$

Divide $$147$$ by $$250$$ and write the remainder:

$${147}\div{250}=0$$

$$\text{remainder}=147$$

We’ve used all our digits, so to continue dividing, let’s write the decimal sign in the quotient and add a $$0$$ to the remainder:

$$147\div250=0{.}$$

$$\text{remainder}=1470$$

Now we’ll divide the remainder $$1470$$ by the divisor $$250$$. Then we’ll write the result after the decimal sign and determine the remainder:

$$147\div250=0.5$$

$$\text{remainder}=220$$

Since the remainder is less than the divisor, we need to write a $$0$$ next to the remainder again:

$$147\div250=0.5$$

$$\text{remainder}={220}0$$

Time to divide again! This time, we’ll divide the remainder $$2200$$ by the divisor $$250$$, writing the result after the decimal sign. Once again, we’ll need to determine a remainder:

$$147\div250=0.58$$

$$\text{remainder}={200}$$

You guessed it — we’re writing a $$0$$ next to the remainder again:

$$147\div250=0.58$$

$$\text{remainder}={200}0$$

This time, when we divide $$2000$$ by the divisor $$250$$ and write our result after the decimal sign, it seems like we’ve found what we need:

$$147\div250=0.588$$

$$\text{remainder}=0$$

Our remainder is $$0$$, so we’re finally done! Here’s our result:

$$147\div250=0.588$$

In summary, you can convert any fraction into a decimal by using this method:

## Study summary

1. Divide the numerator by the denominator.
2. Divide the numbers.

## Do it yourself!

Converting fractions into decimals is a simple process, but that doesn’t mean you shouldn’t practice! Try these problems to make sure you really understand.

Rewrite a fraction as a decimal:

1. $$\frac{5}{8}$$
2. $$\frac{3}{10}$$
3. $$\frac{81}{200}$$
4. $$\frac{73}{250}$$

Solutions:

1. $$0.625$$
2. $$0.3$$
3. $$0.405$$
4. $$0.292$$

If you’re still struggling through the solving process, that’s totally okay! Stumbling a few times is actually good for learning. If you get too stuck or lost, 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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