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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….
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