# Percentages, Decimals and Fractions

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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.