Fractions and decimals

Converting a fraction to a decimal

To change a fraction to a decimal, you divide the top number by the bottom number. (Divide the numerator by the denominator.)

Example

To convert ³/₈ to a decimal, we calculate 3 ÷ 8

so ³/₈ = 0.375

Some decimals will terminate (end) like the example above, but many will not.

For example ²/₇ does not terminate.

There are some fraction/decimal equivalents that you should be familiar with:

• ¹/₂ = 0.5
• ¹/₄ = 0.25
• ³/₄ = 0.75
• ¹/₃ = 0.333333...

  or

Converting a decimal into a fraction

If the decimal terminates (ends), the denominator will be 10, or 100, or 1000 or… (depending on the number of decimal places).

0.5 means 'five tenths’, so 0.5 = ⁵/₁₀ = ¹/₂

0.45 means '45 hundredths', so 0.45 = ⁴⁵/₁₀₀ = ⁹/₂₀

0.240 means ‘240 thousandths’, so 0.240 = ²⁴⁰/₁₀₀₀ = ⁶/₂₅

etc

If the decimal repeats with a single digit, the denominator will be 9:

0.2222222... = ²/₉

0.4444444... = ⁴/₉

0.6666666... = ⁶/₉ = ²/₃

If the decimal repeats with two digits, the denominator will be 99:

0.24242424... = ²⁴/₉₉

etc

If the decimal does not repeat at all it is known as an irrational number, and you cannot write it as a fraction.