**Convert Between Mixed Numbers and Decimals** *KS3 Revision*

## What you need to know

**Things to remember:**

- Knowing basic fraction and decimal equivalents will make this easier.

*What is 3\dfrac{3}{8} as a decimal?*

To start, it is important to remember that 3\dfrac{3}{8}=3+\dfrac{3}{8}, i.e. a whole number and a fraction added together.

*Hint: **If we can learn some basic fraction equivalencies, we can use them to help us convert mixed numbers into decimals.*

* *

\frac{3}{4}=0.75

\frac{1}{2}=0.5

\frac{1}{4}=0.25

\frac{1}{5}=0.2

\frac{1}{8}=0.125

\frac{1}{10}=0.1

\frac{1}{20}=0.05

\frac{1}{50}=0.02

\frac{1}{100}=0.01

Now that we have these we can try and convert our mixed number into a decimal. We will do this in three steps.

**Step 1: **Choose the relevant fraction and decimal equivalent

Our mixed number is using eighths, so we want to use the equivalent decimal.

\frac{1}{8}=0.125

**Step 2:** Using the equivalent decimal in **Step 1**, convert your fraction into a decimal.

3\times\frac{1}{8}=3\times0.125

{3}{8}=0.375

**Step 3: **Add the decimal found in **Step 2 **to the whole number part of the mixed number.

3+0.375=3.375

3\frac{3}{8}=3.375

Converting decimals into mixed numbers is a little trickier, but we can follow similar steps as to what we did previously.

*What is 5.3 as a mixed number?*

**Step 1: **Split up your number into the whole number part and a decimal.

5.3=5+0.3

**Step 2:** Choose the relevant fraction and decimal equivalent.

*Hint: **This will get easier with practice and knowing multiples of the decimals and fractions.*

* *

0.3=3\times0.1

But we know that 0.1=\dfrac{1}{10}, so…

0.3=3\times0.1=3\times\frac{1}{10}=\frac{3}{10}

**Step 3: **Put the whole number part and fraction found in **Step 2** together.

5.3 =5\frac{3}{10}

## Example Questions

**Question 1:** What is 7\dfrac{2}{5} as a decimal?

**Step 1: **Choose the relevant fraction and decimal equivalent

Our mixed number is using fifths, so we want to use the equivalent decimal.

\frac{1}{5}=0.2

**Step 2:** Using the equivalent decimal in **Step 1**, convert your fraction into a decimal.

2\times\frac{1}{5}=2\times0.2

{2}{5}=0.4

**Step 3: **Add the decimal found in **Step 2 **to the whole number part of the mixed number.

7+0.4=7.4

7\frac{2}{5}=7.4

**Question 2:** What is 9.75 as a mixed number?

**Step 1: **Split up your number into the whole number part and a decimal.

9.75=9+0.75

**Step 2:** Choose the relevant fraction and decimal equivalent.

*Hint: **This will get easier with practice and knowing multiples of the decimals and fractions.*

* *

0.75=\frac{3}{4}

**Step 3: **Put the whole number part and fraction found in **Step 2** together.

9.75 =9\frac{3}{4}