# PERCENTAGES TO DECIMALS

Converting percentages to decimals you must remember

1=100%

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

1. Write out what 100% is
2. Write out what we know
3. Keep % on one side

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

2. Write out what we know            31%=x

(Keep the % sign on the same side)

(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)

(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)

(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)

(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