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©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

Fraction to Recurring Decimals 1 2 2 1 1 2 1 2 1 2 Divide Numerator by Denominator . . . And so on 9 1. 0 0 0 0 0 ) 9 2. 0 0 0 0 0 ) 1 2 1 2 1 2 1 2 1 9 5 9 = 0.111111… = 0.1 = 0.55555… = 0.5 2 9 6 9 = 0.22222… = 0.2 = 0.66666… = 0.6 3 9 7 9 = 0.33333… = 0.3 = 0.77777… = 0.7 4 9 8 9 = 0.44444… = 0.4 = 0.8888… = 0.8 Use your calculator for the following, 2

Fraction to Recurring Decimals Click a Disc 2 3 = 0.6 1 7 = 0.142857 2 11 = 0.18 1 13 = 0.076923 1 3 = 0.3 4 7 = 0.571428 1 6 = 0.16 22 7 = 3.142857  

Recurring Decimals to Fractions Change 0.1 into a fraction. Method 1: Use your Calculator. Method 2: 10x = 1 .111111111… - x = 0.111111111… Multiply by 10 Subtract 9x = 1 9 9 Solve Equation 1 x = 9

Recurring Decimals to Fractions Change 0.13 into a fraction. Method 1: Use your Calculator. Method 2: 10x = 1 .33333… - x = 0. 1 3333… Multiply by 10 Subtract 9x = 1.3 x10 9 9 x10 Solve Equation 13 x = 90

Recurring Decimals to Fractions Change 0.19 into a fraction. 100x = 19 .191919… - x = 0.191919… Multiply by 100 Subtract 99x = 19 99 99 Solve Equation 19 x = 99

Recurring Decimals to Fractions Change 0.319 into a fraction. 100x = 31 . 9 191919… - x = 0. 3 191919… Multiply by 100 Subtract 99x = 31.6 x10 99 99 x10 Solve Equation 316 x = 99

Recurring Decimals to Fractions Change 0.201 into a fraction. 1000x = 201 .201201… - x = 0.201201… Multiply by 1000 Subtract 999x = 201 999 999 Solve Equation 201 x = 999

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) 0.0876 Note the different ways of writing recurring decimals.