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 รท 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.

Answer: 0.825

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

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