## Conversions

Fractions, decimals and percentages are all ways of expressing numbers. Each can be converted from one to another.

Below are some of the commonly used percentages, decimals and fractions.

 Percentages Decimals Fractions 5% 0.05 5/100 =1/20 10% 0.1 10/100 = 1/10 15% 0.15 15/100 = 3/20 20% 0.2 20/100 = 1/5 25% 0.25 25/100 = 1/4 30% 0.3 30/100 = 3/10 40% 0.4 40/100 = 2/5 50% 0.5 50/100 = 1/2 60% 0.6 60/100 = 3/5 70% 0.7 70/100 = 7/10 75% 0.75 75/100 = 3/4 80% 0.8 80/100 = 4/5 90% 0.9 90/100 = 9/10 100% 1.0 100/100 = 1

### Methods of Conversion

Fractions to Decimals

To convert a fraction into a decimal, divide the numerator by the denominator.
e.g. 34 = 3 ÷ 4 = 0.75
212 = 52 = 5 ÷ 2 = 2.5

Decimals to Fractions

To convert a decimal into a fraction, put the digits after the decimal point as the numerator, and put 10, 100, 1000 ... (depending on the number of decimal places) as the denominator. Then simplify the fraction whenever possible.
 e.g. 0.75 = 75⁄100 = 3⁄4 0.4 = 4⁄10 = 2⁄5

Decimals to Percentages

To convert a decimal to a percentage, multiply the decimal by 100.

This is done by moving the decimal point two places to the right.

 e.g. 0.25 = 0.25 × 100% = 25% 1.625 = 1.625 × 100% = 162.5%

Percentages to Decimals

To convert a percentage to a decimal, divide the percentage by 100 .

This is done by moving the decimal point two places to the left.

 e.g. 35% = 35 ÷ 100 = 0.35 6% = 6 ÷ 100 = 0.06

Fractions to Percentages

To convert a fraction to a percentage, multipy the fraction by 100.
e.g. 14 = 14 × 100% = 25%
98 = 98 × 100% = 112.5%

Percentages to Fractions

To convert a percentage to a fraction, divide the percentage by 100.

This is done by changing the denominator to 100 and then simplifying, if possible.

e.g. 30% = 30100 = 310
150% = 150100 = 32

Try this activity to practice converting between decimals, fractions and percentages.

### Summary

 >-----> Fractions Decimals Percentages Fractions Divide numerator by denominator Multiply by 100 Decimals Put over 10, 100 or 1000... Multiply by 100 Percentages Divide by 100 Divide by 100

For help checking your decimal <---> fraction conversions: 