When a fraction is written as a number, it either recurs or terminates (it is NOT and irrational number) For example

The recurring, or repeating part has a bar over it, or it can be written with a dot over the first and last repeating digits:

There is a simple rule to know if a fraction will recur. You look at the bottom part of the fraction, and decompose it to the basic prime numbers.

For example, if the fraction is 9 / 25  you write it as 9 / 5×5    if the fraction is 3/20  you write it as   3 / 2×2x5     so you break it down to the lowest possible terms. Notice that all the terms we have broken down so far are either TWOS or FIVES therefore, IT WILL NOT RECUR.

What about this one  2 / 9   will it recur?

2 / 9  =   2 / 3×3        

There are now threes. It is not ONLY TWOS or FIVES, therefore it WILL RECUR:

2 / 9 =  0.22222222….

QUESTION 1: Convert  3 / 8  into a decimal. Will this recur? To do this we use Long division:

QUESTION 2: Convert 8 / 33 into a decimal. Long division again:

Now to convert this back to the fraction, we use the following working:

What about 0.06 81 81 81 …? This is a slightly harder working, but very similar, when you break it down:

Here is a last one. Do the Long division for 2 / 7   try it before you look at the working below. It is good practice.