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 |

^{1}⁄_{20} |
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^{1}⁄_{10} |
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^{3}⁄_{20} |
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^{1}⁄_{5} |
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^{1}⁄_{4} |
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^{3}⁄_{10} |
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^{2}⁄_{5} |
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^{1}⁄_{2} |
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^{3}⁄_{5} |
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^{7}⁄_{10} |
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^{3}⁄_{4} |
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^{4}⁄_{5} |
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^{9}⁄_{10} |
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### Methods of Conversion

**Fractions to Decimals**

To convert a fraction into a decimal, divide the numerator by the denominator.

e.g.

^{3}⁄_{4}= 3 ÷ 4 = 0.752^{1}⁄_{2}=^{5}⁄_{2}= 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.

Any integers remain in front of the decimal point.

e.g. 0.4 = ^{4}⁄_{10}=^{2}⁄_{5}0.75 = ^{75}⁄_{100}=^{3}⁄_{4}

**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.^{1}⁄_{4}=^{1}⁄_{4}× 100% = 25%^{9}⁄_{8}=^{9}⁄_{8}× 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% =

^{30}⁄_{100}=^{3}⁄_{10}150% =

^{150}⁄_{100}=^{3}⁄_{2}

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

### Summary

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FractionsDecimalsPercentagesFractionsDivide numerator by denominator Multiply by 100 DecimalsPut over 10, 100 or 1000... Multiply by 100 PercentagesDivide by 100 Divide by 100