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`
