In the field of maths, fractions, percentages and decimals represent the same thing - numbers less than 1. For KS3 Maths you should know the equivalences between fractions, decimals and percentages. All three types of numbers are used in day-to-day life and it's useful to be able to change from one to the other.

Any number can be written as a fraction, a percentage or a decimal. Let's look at a simple example: three quarters. As a fraction, the simplest way to write three quarters is as ^{3}⁄_{4}. Percentages write fractions as 100ths. One quarter of a hundred is 25 so three quarters as a percentage would be 25 x 3 = 75%. Decimals use tenths and hundredths. So, 75 hundredths (^{3}⁄_{4}) would be written as 0.75. It's all quite simple - once you've got the hang of it!

To help you understand how fractions work, take a look at the Fractions - Numerical Quantities article.

1.

What is 3/5 written as a percentage?

30%

60%

75%

90%

Three-fifths of 100 is 60

2.

How would you write 0.9 as a fraction?

1/9

3/9

7/9

9/10

9 and 10 have only one common factor - 1, so 9/10 is the simplest way to write this fraction

3.

How is 75% written as a decimal?

0.5

0.7

0.72

0.75

To convert percentages to decimals simply move the digits two places to the right

4.

How is 0.25 written as a fraction?

1/4

1/3

1/2

2/3

0.25 is one-quarter of 1

5.

What is 3/4 written as a percentage?

10%

25%

50%

75%

Three-quarters of 100 is 75

6.

How is 20% written as a fraction?

1/5

1/4

1/3

1/2

100 divided by 20 is 5 so 20% is the same as 1/5

7.

How would you write 5.25 as a fraction?

1/5

5^{2}⁄_{5}

5^{1}⁄_{4}

5%

The 5 is a whole number - only the numbers after the decimal need to be made into a fraction

8.

What is 3/5 written as a decimal?

0.3

0.5

0.6

0.8

In decimals 1/5 is 0.2 so multiply 0.2 by 3 for the answer

9.

What is 3/4 written as a decimal?

0.25

0.5

0.75

0.80

Three-quarters of 1 is 0.75

10.

How is 166% written as a decimal?

1

1.6

1.66

1.67

To convert percentages to decimals simply move the digits two places to the right