## 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.2/5, and so is a percentage, except that the denominator is always 100 eg. 40%=40/100. To change any fraction or percentage into a decimal we actually carry out the division, so40%=40/100 =0.4.

The table below shows some examples of this equivalence.

 Fraction Decimal Percentage,% 2/25 0.08 8 7/50 0.14 14 3/10 0.3=0.30 30 3/8 0.375 37.5 7/20 0.35 35 1/1 1 100 47/40 1.175 117.6 2=2/1 2 200 3/2 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 2/1.

• 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/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.