Converting Between Percentages and decimals | KS3 Maths Resources

## What you need to know

Things to remember:

• To turn a percentage into a decimal you have to divide by 100
• To turn a decimal into a percentage you have to multiply by 100.
• The best way to improve in this topic is practice multiplying and dividing by 100!

To start off with, let’s look at how we get from 100% to other percentages.

Percentage

100%

$\div2$ 50%

$\div4$ 25%

$\div5$ 20%

$\div10$ 10%

$\div20$ 5%

$\div50$ 2%

$\div100$ 1%

But, we know that 100% represents a whole, or 100%=1, so we can use these same divisions to find some basic decimals.

Percentage Decimal

100% 1

$\div2$ 50% 0.5

$\div4$ 25% 0.25

$\div5$ 20% 0.2

$\div10$ 10% 0.1

$\div20$ 5% 0.05

$\div50$ 2% 0.02

$\div100$ 1% 0.01

When comparing these percentages and decimals, it is important to notice that all that has actually happened is, we have divided by 100.

$$100\div100=1$$

$$50\div100=0.5$$

$$20\div100=0.2$$

$$5\div100=0.5$$

All we need to do is remember that when we divide by 100, we move all digits two places to the right.

$$77\%\div100 \rightarrow7.7\rightarrow0.77$$

$$77\%=0.77$$

$$123\%\div100 \rightarrow12.3\rightarrow1.23$$

$$123\%=1.23$$

$$3.1\%\div100 \rightarrow0.31\rightarrow0.031$$

$$3.1\%=0.31$$

How about if we want to go in the opposite direction and turn a decimal into a percentage? Well, we do the opposite, we multiply by 100!

Hint: Remember, when we multiply by 100, we move all the digits to the left two places.

$$0.13\times100\rightarrow1.3\rightarrow13$$

$$0.13=13\%$$

$$1.67\times100\rightarrow16.7\rightarrow167$$

$$1.67=167\%$$

$$0.002\times100\rightarrow0.02\rightarrow0.2$$

$$0.002=0.2\%$$

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## Example Questions

$$37.6\%\div100 \rightarrow3.76\rightarrow0.376$$

$$37.6\%=0.376$$

$$2.34\times100\rightarrow23.4\rightarrow234$$

$$2.34=234\%$$

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