What is 0.3 repeating as a fraction in simplest form?

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

To convert a recurring decimal to a fraction:

Let ##x = 0.333333..." "larr## one digits recurs

##10x= 3.3333333...##

##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 ##subtract ## 100x-x = 99x##

##99x = 75.00000...##

##x = 75/99##

##x = 25/33## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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...## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~