# Percentage to decimals

Converting percentage to decimals you must remember

`100%=1`

This will then help you remember that:

`50%=0.5`

`25%=0.25`

`75%=0.75`

`33\1/3%=0.3dot3`

`66\2/3%=0.6dot6`

`10%=0.1`

`20%=0.2`

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

**Example 1**

Express `0.31` as a percentage

to do this remember `100%=1`

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 `x%=0.31`

3. Put the divide sign in

`(100%)/(x%)=1/0.31`

Now work out what `x` is

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

`(cancelx100)/cancelx=1/0.31timesx`

`100=x/0.31`

Multiply both sides by `0.31` to get `x` on its own.

`0.31times100=(xcancel0.31)/cancel0.31`

`x=100times0.31`

`x=31%`

**Example 2**

Convert `0.125` to a `%`

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

2. Write out what we know `x%=0.125`

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

3. Put the divide sign in

`(100%)/(x%)=1/0.125`

Now work out what `x` is

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

`(cancelx100)/cancelx=1/0.125timesx`

`100=x/0.125`

Multiply both sides by `0.125` to get `x` on its own.

`0.125times100=(xcancel0.125)/cancel0.125`

`x=100times0.125`

`x=12.5%`

**Example 3**

What is `1.04` converted to a `%`

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

2. Write out what we know `x%=1.04`

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

3. Put the divide sign in

`(100%)/(x%)=1/1.04`

Now work out what `x` is

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

`(cancelx100)/cancelx=1/1.04timesx`

`100=x/1.04`

Multiply both sides by `1.04` to get `x` on its own.

`1.04times100=(xcancel1.04)/cancel1.04`

`x=100times1.04`

`x=104%`

**Example 4**

What is `0.005` converted to a `%`

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

2. Write out what we know `x%=0.005`

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

3. Put the divide sign in

`(100%)/(x%)=1/0.005`

Now work out what `x` is

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

`(cancelx100)/cancelx=1/0.005timesx`

`100=x/0.005`

Multiply both sides by `0.005` to get `x` on its own.

`0.005times100=(xcancel0.005)/cancel0.005`

`x=100times0.005`

`x=0.5%`