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 practise converting fractions, decimals and percentages you can play this quiz. Take your time and read each question carefully!

1.

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

2.

How is 0.25 written as a fraction?

1/4

1/3

1/2

2/3

0.25 is one-quarter of 1

3.

What is 3/5 written as a percentage?

30%

60%

75%

90%

Three-fifths of 100 is 60

4.

What is 3/4 written as a decimal?

0.25

0.5

0.75

0.80

Three-quarters of 1 is 0.75

5.

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

6.

What is 3/4 written as a percentage?

10%

25%

50%

75%

Three-quarters of 100 is 75

7.

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

8.

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

9.

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

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

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