Converting decimals to fractions and percentages

Converting decimals to fractions

To convert a decimal to a fraction, use place value. The first number after the decimal place is worth tenths, the next is worth hundredths, the next thousandths and so on.

Example

What is 0.7 as a fraction?

HundredsTensUnits.TenthsHundredthsThousandths
0.7

The 7 represents tenths, so this can be written as \frac{7}{10}. This fraction cannot be simplified or cancelled down so it is the final answer.

Question

What is 0.46 as a fraction?

HundredsTensUnits.TenthsHundredthsThousandths
0.46

0.46 is worth 46 hundredths which is written as \frac{46}{100}. Taking out a common factor of 2, this simplifies to \frac{23}{50}.

0.46 is \frac{23}{50} as a fraction.

Converting decimals to percentages

Once a number is written as a decimal, it is easy to convert it to a percentage. Remember that 'per cent' means 'per hundred', so converting from a decimal to a percentage can be done by multiplying by 100 (move the decimal place two places to the right).

0.375 as a percentage = 0.375 \times 100 = 37.5 \%