A recurring decimal is just a decimal that repeats forever. Some fractions can only be expressed as recurring decimals.

E.g. 1/3 = 0.333333333…, 24/99 = 0.24242424…

They are often written with little dots over them to indicate how they recur (as shown above).**Turning Recurring Decimals Into Fractions**

To do this you’re going to need algebra (sorry about that!).**Example:** Write 0.234234234234… as a decimal.

Let x = 0.234234234…

Multiply by 10,100, 1000 or whatever power of ten to get the recurring bit past the decimal point. So here you would multiply by 1000.

So 1000x = 234.234234234….

So now just take x away from 1000x

999x = 234.234234234… – 0.234234234… = 234

999x = 234

So x = 234/999

Simplify it down.

x = 26/11

But it’s a bit harder when the recurring bit doesn’t come directly after the decimal.**Example:** Turn 0.166666666… into a fraction.

So let x = 0.166666666…

Multiply by 10,100, 1000 or whatever power of ten to get one full repeated lump past the decimal point. So here you would multiply by 100.

100x = 16.66666666…

Subtracting x isn’t going to help here….you’ll end up with a horrible number….but what if you subtracted 10x?

10x = 1.66666666…

So 90x = 16.66666666… – 1.66666666… = 15

So x = 15/90 = 1/6

Neat huh?**Turning Fractions Into Recurring Decimals**

Easy with a calculator…without it you are going to have to do some long division until you spot the recurring pattern.