Terminating Decimals and Fractions

## Terminating Decimals and Fractions

A fraction is really a division: for example: frac(1)(2) is another way of writing 1 ÷ 2, where the horizontal fraction line means divide by. Carrying out the division gives 0.5 as a decimal.

frac(1)(4) = 0.25. Multiply this fraction by 3: 3 x frac(1)(4) = frac(3)(4), or 3 x 0.25 = 0.75.

Many fractions give a terminating decimal; the division ends after a number of decimal places.

Some fractions do not terminate and the number can be divided forever. For example, frac(1)(3) gives a result of 0.333333... This is known as a recurring decimal.

Decimals can be changed into fractions by determining the lowest place for the decimal. For example, 0.46 has a lowest place value of hundredths, so can be written as frac(46)(100) (and simplified to frac(23)(50)).

## Example 1

Write 0.085 as a fraction. Give the answer in its simplest form.

The lowest place value is in the 1/1000ths.

Divide 85 by 1000 to make the fraction frac(85)(1000).

Divide both numerator and denominator by 5 to simplify to frac(17)(200).

Answer: frac(17)(200)

## Example 2

Write frac(5)(8) as a decimal.

frac(1)(8) = 0.125. Multiply 0.125 by 5 to get 0.825.