1. ©2009 – Not to be sold/Free to use
Stage 5
Year 9
Rational
Numbers
Recurring
Decimals
Press Ctrl-A
©2009 – Not to be sold/Free to use

2. Fraction to Recurring Decimals1 2 2 1 1 2 1 2 1 2
Divide Numerator by Denominator
. . . And so on ) ) 1 2 1 2 1 2 1 2 1 9 5 9 = …
= 0.1 = …
= 0.5 2 9 6 9 = …
= 0.2 = …
= 0.6 3 9 7 9 = …
= 0.3 = …
= 0.7 4 9 8 9 = …
= 0.4 =
0.8888…
= 0.8
Use your calculator for the following, 2

3. Fraction to Recurring Decimals
Click a Disc 2 3
= 0.6 1 7 = 2 11
= 0.18 1 13 = 1 3
= 0.3 4 7 = 1 6
= 0.16 22 7 =
 

4. Recurring Decimals to Fractions
Change 0.1 into a fraction.
Method 1:
Use your Calculator.
Method 2:
10x = … -
x = …
Multiply by 10
Subtract
9x = 1 9 9
Solve Equation 1
x = 9

5. Recurring Decimals to Fractions
Change 0.13 into a fraction.
Method 1:
Use your Calculator.
Method 2:
10x = … -
x = …
Multiply by 10
Subtract
9x = 1.3
x10 9 9
x10
Solve Equation 13
x = 90

6. Recurring Decimals to Fractions
Change 0.19 into a fraction.
100x = … -
x = …
Multiply by 100
Subtract
99x = 19 99 99
Solve Equation 19
x = 99

7. Recurring Decimals to Fractions
Change into a fraction.
100x = … -
x = …
Multiply by 100
Subtract
99x = 31.6
x10 99 99
x10
Solve Equation
316
x = 99

8. Recurring Decimals to Fractions
Change into a fraction.
1000x = … -
x = …
Multiply by 1000
Subtract
999x = 201
999
999
Solve Equation
201
x =
999

9. Note the different ways of writing recurring decimals.
Recurring Decimals to Fractions
Try these and check them
on your calculator.
a) 0.7
e) 0.078
b) 0.18
f) 0.234
c) 0.203
g) 0.381
d) 0.34 h)
Note the different ways of
writing recurring decimals.