Brush up your maths: Percentages

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.

Exercise: percentages

What is 20% of 150?

What is 30% of 764.86 to two decimal places?

Check answer to percentages exercise.

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.

Exercise: percentages and decimals

What is 2½% as a decimal?

What is 0.15 as a percentage?

Check answer to percentages and decimals exercise.

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.

Exercise: percentage increase and decrease

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.


Back to Brush up your maths main menu.

To Martin Bland's M.Sc. index.

To Martin Bland's home page.

This page maintained by Martin Bland.
Last updated: 2 October, 2007.

Back to top.