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Brush up your maths: Percentages

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Percentages

A percentage is a fraction out of 100.
For example, 10% is the same as 10/100.
So taking 10% of something is the same as multiplying it by the fraction

10

–––

100

If we take 10% of 450 we get

10

––– × 450 = 45

100

It is the same as multiplying by 10 then dividing by 100,
shifting the decimal point two places to the left:
450 × 10 = 4500, then shift the decimal point to give 45.0.

In the same way, 17½% of 450 is 450 × 17½ ÷ 100 =
7875.0 ÷ 100 = 78.75.

What is 20% of 150?

What is 30% of 764.86 to two decimal places?

Check answer to percentages exercise.

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Converting percentages to decimals and decimals to percentages

To change a decimal to a percentage, multiply it by 100.
For example 0.05 is equivalent to 5%, because 0.05 × 100 = 5.
In the same way, 0.175 is equivalent to 17.5% or 17½%,
because 0.175 × 100 = 17.5.

To change a percentage to a decimal, divide it by 100.
For example 20% is equivalent to 0.20, because 20 ÷ 100 = 0.20.

What is 2½% as a decimal?

What is 0.15 as a percentage?

Check answer to percentages and decimals exercise.

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Percentage increase and decrease

If we increase something by a percentage,
we calculate that percentage and add it to the original number.
For example, £1000 in a building society offering 5% interest will grow to £1050
over a year.
We can do this by 5% of 1000 = 1000 × 5 ÷ 100 = 5000 ÷ 100 = 50.
We then add 50 to 1000: 1000 + 50 = 1050.

We can also do this by changing the percentage to a decimal, 5% = 0.05,
and adding this to 1.00, 1.00 + 0.05 = 1.05.
We then multiply by this number: 1000 × 1.05 = 1050.

If we decrease something by a percentage,
we calculate that percentage and subtract it from the original number.
For example, £1000 income minus 40% tax will leave £600.
We can do this by 40% of 1000 = 1000 × 40 ÷ 100 = 40000 ÷ 100 = 400.
We then subtract 400 from 1000: 1000 – 400 = 600.

We can also do this by changing the percentage to a decimal, 40% = 0.40,
and subtracting this from 1.00, 1.00 – 0.40 = 0.60.
We then multiply by this number: 1000 × 0.60 = 600.

How much would a plumber's bill for £452 before tax be after 17½% VAT was added?

How much would a restaurant bill for £62.50 be after a 10% loyalty card
bonus was subtracted?

Check answer to percentage increase and decrease exercise.

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Last updated: 2 October, 2007.

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