Question

What is 0.3 repeating as a fraction in simplest form?

Answer 1

`0.bar 3 = 1/3`

Explanation:

Take a calculator and divide:

`1 div 3` and the answer will be `0.333333...`

Answer 2

`0.bar3 = 3/9 = 1/3`

Explanation:

To convert a recurring decimal to a fraction:

Let `x = 0.333333..." "larr` one digit recurs

`10x= 3.3333333..." "larr` multiply by 10

`9x = 3.0000000...." "larr` subtract `10x-x`

`x = 3/9 = 1/3`

If 2 digits recur : for example `0.757575...`

`" "x = 0.757575...`
`100x = 75.757575...." " larr`multiply by 100

`99x = 75.00000..." :larr`subtract `100x-x = 99x`

`x = 75/99`

`x = 25/33`
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It is a good idea to know the conversion of some of the common fractions to decimals by heart.

This includes:
`1/2 =0.5" "1/4 = 0.25" "3/4=0.75`

`1/5=0.2" "2/5=0.4" "3/5=0.6" "4/5=0.8`

`1/8=0.125" "3/8=0.375" "5/8=0.625" "7/8=0.875`

These are all terminating decimals.

The recurring decimals which are useful to know are:

`1/3 =0.3333..." "2/3 = 0.6666....`

`1/6 = 0.16666..." "5/6 = 0.83333...`
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