3. Recurring decimals = 0.3333333333333…… 3 1

4. Recurring decimals … it keeps going on, it will never stop – we say it recurs. = 0.3333333333333…… 3 1

5. Recurring decimals … it keeps going on, it will never stop – we say it recurs. = 0.3333333333333…… 3 We can write it in mathematical shorthand as: 1

6. Recurring decimals … it keeps going on, it will never stop – we say it recurs. = 0.3333333333333…… 3 We can write it in mathematical shorthand as: 1 . 0.3333333333333…… = 0.3

7. 0.12121212121212… Is another recurring decimal

8. 0.12121212121212… Is another recurring decimal This can be written as 0.12 . .

9. 0.12121212121212… Is another recurring decimal This can be written as 0.12 . . In the same way 0.12341234123412341234 =

10. 0.12121212121212… Is another recurring decimal This can be written as 0.12 . . In the same way 0.12341234123412341234 = . . 0.1234

13. Recurring decimals as exact fractions For example Write 0.3 as an exact decimal Here only one 3 is recurring So the numerator is 3 3

14. Recurring decimals as exact fractions For example Write 0.3 as an exact decimal Here only one 3 is recurring So the numerator is 3 3 3 There is one digit in the numerator so we have one 9 in the denominator 9

15. Recurring decimals as exact fractions For example Write 0.3 as an exact decimal Here only one 3 is recurring So the numerator is 3 3 3 1 There is one digit in the numerator so we have one 9 in the denominator 9 This can then be cancelled down to be 3

16. . . 0.12

17. . . 0.12 12

18. . . 0.12 2 digits 12

19. . . 0.12 2 digits 99 12

20. . . 0.1234

21. . . 0.1234 1234

22. . . 0.1234 1234 4 digits

23. . . 0.1234 1234 4 digits 9999

24. . . 0.1234 1234 4 digits 9999

25. . . 0.12 2 digits 99 12 . . 0.1234 1234 4 digits 9999

26. . . 0.12 2 digits 99 12 . . 0.1234 1234 4 digits 9999

27. Now try these Write the following using the dot notation then convert them into exact fractions. 0.111111111…. 0.4343434343 …. 0.765765765 …. 0.237823782378237…

28. Now try these Write the following using the dot notation then convert them into exact fractions. 0.111111111…. 0.4343434343 …. 0.765765765 …. 0.237823782378237… . 0.1 0.43 0.765 0.2378 . . . . . .

29. Now try these Write the following using the dot notation then convert them into exact fractions. 0.111111111…. 0.4343434343 …. 0.765765765 …. 0.237823782378237… . 0.1 0.43 0.765 0.2378 . . . . 1 43 99 765 2378 999 . . 9 9999