A recurring decimal is one that repeats itself forever. We use dots above the decimal numbers to show how it repeats. Look at the following table to see how the notation works.

Remember that for **three recurring numbers**, we only place dots on the *first *and *last *digits.

**Example 1
**

_{
}Write the following recurring decimal as a fraction:

**Answer **

Let x = 0.5454545454545454....

Then 100x = 54.5454545454545454...

Now subtract both sides to get rid of the recurring part of the decimal, leaving:

99x = 54

So x = 54/99 =** 6/11 **in its lowest terms.

**Example 2
**

_{
}Write the following recurring decimal as a fraction:

**Answer **

Let x = 0.405405405405....

Then 1000x = 405.405405405405...

Notice that because 3 digits recur, we have to find **1000x **not 100x.

Now subtract both sides to get rid of the recurring part of the decimal, leaving:

999x = 405

So x = 405/999 =** 15/37 **in its lowest terms.

**Notice that....**

_{ } = 5/9

_{} = 54/99

_{} = 405/999