 Convert Between Mixed Numbers and Decimals | KS3 Maths Resources

## 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

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.

$$7+0.4=7.4$$

$$7\frac{2}{5}=7.4$$

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.

$$9.75 =9\frac{3}{4}$$

## KS3 Maths Revision Cards

(77 Reviews) £8.99
• All of the major KS2 Maths SATs topics covered
• Practice questions and answers on every topic