Recurring DecimalsAll recurring decimals can be written as fractionsThey are

‘rational numbers’

Recurring DecimalsTo write recurring

decimals as fractions, we use a simple multiplying

method…

Recurring Decimalse.g. 0.333333333…

Let x = 0.333333333…

Then 10x = 3.333333…

We do a subtraction…

Recurring Decimals10x = 3.33333333… - x = 0.33333333… 9x = 3

X = 3 = 1 9 3

Recurring Decimalse.g. 0.565656…

Let x = 0.5656565…

100x = 56.56565656…

We do a subtraction…

Recurring Decimals100x =

56.56565656… - x = 0.565656565 99x = 56X = 56

99

Recurring DecimalsReminder:

Recurring decimals are written by using a dot:

.e.g. 0.3333333…. = 0.3

Now you try

• Convert the decimals to fractions– 0.545454…..

– 0.599999….