1

RecurringRecurringDecimalsDecimals

Press Ctrl-APress Ctrl-A©2009 – Not to be sold/Free to use

Stage 5Stage 5Year 9Year 9

2

Fraction to Recurring Decimals

2

19

= 0.111111…

= 0.1

29

= 0.22222…

= 0.2

39

= 0.33333…

= 0.3

49

= 0.44444…

= 0.4

59

= 0.55555…

= 0.5

69

= 0.66666…

= 0.6

79

= 0.77777…

= 0.7

89

= 0.8888… = 0.8

9 1. 0 0 0 0 0 )1

111

111

111

11

9 2. 0 0 0 0 0 )2

222

222

222

2200 21

Divide Numerator by DenominatorDivide Numerator by Denominator. . . And so on. . . And so on

Use your calculator for the following,

3

Fraction to Recurring Decimals

17

= 0.14285723

= 0.6

47 = 0.571428

113= 0.076923

211= 0.18

13

= 0.3

16 = 0.16 22

7= 3.142857

Click a DiscClick a Disc

4

Recurring Decimals to Fractions

Method 1:Use your Calculator.

Method 2:

x = 0.111111111…Multiply by 1010x = 1 .111111111…

Subtract--

9x = 1Solve Equation9 9

x = 19

5

Recurring Decimals to Fractions

Method 1:Use your Calculator.

Method 2:

x = 0. 1 3333… Multiply by 1010x = 1 .33333…

Subtract--

9x = 1.3Solve Equation9 9

x = 1390

x10x10

x10x10

6

Recurring Decimals to Fractions

x = 0.191919… Multiply by 100100x = 19 .191919…

Subtract--

99x = 19Solve Equation99

x = 1999

99

7

Recurring Decimals to Fractions

x = 0. 3 191919… Multiply by 100100x = 31 . 9 191919…

Subtract--

99x = 31.6Solve Equation99

x = 31699

99x10x10

x10x10

8

Recurring Decimals to Fractions

x = 0.201201… Multiply by 10001000x = 201 .201201…

Subtract--

999x = 201Solve Equation999

x = 201999

999

9

Recurring Decimals to Fractions

a) 0.7

b) 0.18

c) 0.203

d) 0.34

e) 0.078

f) 0.234

g) 0.381

h) 0.0876

Note the different ways ofwriting recurring decimals.