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

2. 2 Fraction to Recurring Decimals 2 1919 =0.111111…= 0.1 2929 =0.22222…= 0.2 3939 =0.33333…= 0.3 4949 =0.44444…= 0.4 5959 =0.55555… = 0.5 6969 =0.66666…= 0.6 7979 =0.77777…= 0.7 8989 =0.8888…= 0.8 9 1. 0 0 0 0 0 ) 1 1 1 1 1 1 1 1 9 2. 0 0 0 0 0 ) 2 2 2 2 2 2 2 2 0 0 2 1 Divide Numerator by Denominator... And so on Use your calculator for the following,

3. 3 Fraction to Recurring Decimals 1717 = 0.142857 2323 = 0.6 4747 = 0.571428 1 13 = 0.076923 2 11 = 0.18 1313 = 0.3 1616 = 0.16 22 7 = 3.142857      Click a Disc

4. 4 Recurring Decimals to Fractions Method 1: Use your Calculator. Method 2: x = 0.111111111…Multiply by 10 10x = 1.111111111… Subtract - 9x = 1 Solve Equation 99 x = 1 9

5. 5 Recurring Decimals to Fractions Method 1: Use your Calculator. Method 2: x = 0. 1 3333…Multiply by 10 10x = 1.33333… Subtract - 9x = 1.3 Solve Equation 99 x = 13 90 x10 x10

6. 6 Recurring Decimals to Fractions x = 0.191919…Multiply by 100 100x = 19.191919… Subtract - 99x = 19 Solve Equation 99 x = 19 99

7. 7 Recurring Decimals to Fractions x = 0. 3 191919…Multiply by 100 100x = 31. 9 191919… Subtract - 99x = 31.6 Solve Equation 99 x = 316 99 x10 x10

8. 8 Recurring Decimals to Fractions x = 0.201201…Multiply by 1000 1000x = 201.201201… Subtract - 999x = 201 Solve Equation 999 x = 201 999

9. 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 of writing recurring decimals.