How to Do Recurring Fraction Sums

Firstly we need to define recurring decimal as a rational number that does not terminate.

Example 1, 0.444444444...

Example 2, 0.123123123...

A fraction is a number in which the numerator is divided by the denominator. In terminating decimals, the number of decimal places determines if the denominator would be 10, 100 or 1000 for fractions of tenths, hundredths and thousandths respectively.

Recurring decimals are patterned and can be simplified with algebra.

Using Example 1, only 1 digit is repeated

Let x = 0.4444444444...

  10x = 4.4444444444...

Then 10x - x = 4.4444444444... - 0.4444444444...

9x = 4

x = 4/9

Example 2

Let x = 0.123123123...

  10x = 1.231231231...

*which complicate things, we are looking to eliminate all decimal points when we subtract x from this

100x = 12.312312312...

*this does not help either, 3 digits are repeated, so we try

 1000x = 123.123123123...

-       x =      0.123123123...

So we have 999x = 123

Therefore x = 123/999