Percentages, Fractions and Decimals

Percentages, fractions and decimals are essentially the same idea in different forms. A fraction is one whole number divided by another whole number eg.2 over 5, and so is a percentage, except that the denominator is always 100 eg. 40%=40 over 100. To change any fraction or percentage into a decimal we actually carry out the division, so40%=40 over 100 =0.4.

The table below shows some examples of this equivalence.

Fraction

Decimal

Percentage,%

2 over 25

0.08

8

7 over 50

0.14

14

3 over 10

0.3=0.30

30

3 over 8

0.375

37.5

7 over 20

0.35

35

1 over 1

1

100

47 over 40

1.175

117.6

2=2 over 1

2

200

3 over 2

1.5

150

Several things can be noted about the numbers in the table:

  • A whole number is a fraction since we can write for example, 2 as 2 over 1.

  • A percentage greater than 100% is possible – the numerator is greater than the denominator.

  • Given a percentage we can find the fraction by writing the percentage over 100 and the decimal by carrying out the division.

  • Given a decimal we can find the percentage by writing the multiplying by 100.

  • Given a fraction we can find the decimal by carrying out the division and the percentage by multiplying by 100.

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