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.

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

$x=0.5/100$

$x=0.005$