# PERCENTAGES TO DECIMALS

Converting percentages to decimals you must remember

`1=100%`

This will then help you remember that

`0.5=50%`

`0.25=25%`

`0.75=75%`

`0.3dot3=33\1/3%`

`0.6dot6=66\2/3%`

`0.1=10%`

`0.2=20%`

But knowing `1=100%` will also help you solve any inbetween percentages.

**Example 1**

Express `31%` as a decimal

to do this remember `1=100%`

and also read this in conjunction with the section on percentages.

Which states

- Write out what `100%` is
- Write out what we know
- Keep `%` on one side
- Put the divide sign in

1. Write out what `100%` is `100%=1`

2. Write out what we know `31%=x`

(Keep the `%` sign on the same side)

3. Put the divide sign in

`(100%)/(31%)=1/x`

Now work out what `x` is

Multiply by `x` on both sides to get `x` on its own.

`(100%)/(31%)timesx=(1timescancelx)/cancelx`

`100/31timesx=1`

Multiply both sides by `31%` to get `x` on its own.

`100/cancel31timesxtimescancel31=1times31`

`100%x=31`

Divide both sides by `100` to get `x` on its own.

`(cancel100\x)/cancel100=31/100`

`x=31/100`

`x=0.31`

**Example 2**

Convert `12.5%` to a decimal

1. Write out what `100%` is `100%=1`

2. Write out what we know `12½%=x`

(Keep the `%` sign on the same side)

3. Put the divide sign in

`(100%)/(12.5%)=1/x`

Now work out what `x` is

Multiply by `x` on both sides to get `x` on its own.

`(100%)/(12.5%)timesx=(1timescancelx)/cancelx`

`100/12.5timesx=1`

Multiply both sides by `12.5` to get `x` on its own.

`100/cancel12.5timesxtimescancel12.5=1times12.5`

`100x=12.5`

Divide both sides by `100` to get `x` on its own.

`(cancel100\x)/cancel100=12.5/100`

`x=12.5/100`

`x=0.125`

**Example 3**

Convert `104%` to a decimal

1. Write out what `100%` is `100%=1`

2. Write out what we know `104%=x`

(Keep the `%` sign on the same side)

3. Put the divide sign in

`(100%)/(104%)=1/x`

Now work out what `x` is

Multiply by `x` on both sides to get `x` on its own.

`(100%)/(104%)timesx=(1timescancelx)/cancelx`

`100/104timesx=1`

Multiply both sides by `104` to get `x` on its own.

`100/cancel104timesxtimescancel104=1times104`

`100x=104`

Divide both sides by `100` to get `x` on its own.

`(cancel100\x)/cancel100=104/100`

`x=104/100`

`x=1.04`

**Example 4**

Convert `0.5%` to a decimal

1. Write out what `100%` is `100%=1`

2. Write out what we know `0.5%=x`

(Keep the `%` sign on the same side)

3. Put the divide sign in

`(100%)/(0.5%)=1/x`

Now work out what `x` is

Multiply by `x` on both sides to get `x` on its own.

`(100%)/(0.5%)timesx=(1timescancelx)/cancelx`

`100/0.5timesx=1`

Multiply both sides by `0.5` to get `x` on its own.

`100/cancel0.5timesxtimescancel0.5=1times0.5`

`100x=0.5`

Divide both sides by `100` to get `x` on its own.

`(cancel100\x)/cancel100=0.5/100`

`x=0.5/100`

`x=0.005`