Terminating Decimals and Fractions

# Terminating Decimals and Fractions

GCSE(F),

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. Similar calculations can be carried out for a range of fractions.

Many fractions give a terminating decimal; that is, the division can be finished after a number of decimal places. Some fractions do not terminate; that is, the number can be divided forever: for example, frac(1)(3) gives a result of 0.333333... This is known as a recurring decimal.

Multiples of fractions can also be converted into decimals: frac(3)(4) is 3 x frac(1)(4) = or 3 x 0.25 = 0.75.

Decimals can be changed into fractions by determining the lowest place for the decimal, then dividing by that place value. 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).

## Examples

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

Answer: frac(17)(200)

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).

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

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