This document discusses recurring decimals and how to write them as exact fractions. It explains that recurring decimals can be written using dot notation and defines key terms like decimals and fractions. Examples are provided of writing recurring decimals like 0.3 and 0.12 as fractions by placing the recurring digits in the numerator and using 9s in the denominator based on the number of recurring digits. Finally, it prompts working through converting additional recurring decimals to fractions.

1. Recurring decimalsBTEOTSSBAT:Write recurring decimals using the dot notation

2. Change recurring decimals into exact fractionsKey termsDecimalsFractionsRecurringExact

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……3We 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……3We 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 decimalThis can be written as 0.12..

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

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

11. Recurring decimals as exact fractionsRecurring decimals can easily be written as fractions.To do this: place the recurring numbers at the top of the decimal (as the numerator)

12. write as many 9s as there are digits in the numerator as the bottom bit (denominator)Recurring decimals as exact fractionsFor example Write 0.3 as an exact decimal

13. Recurring decimals as exact fractionsFor 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 fractionsFor example Write 0.3 as an exact decimal Here only one 3 is recurring So the numerator is 3 3 3There is one digit in the numerator so we have one 9 in the denominator9

15. Recurring decimals as exact fractionsFor example Write 0.3 as an exact decimal Here only one 3 is recurring So the numerator is 3 3 3 1There is one digit in the numerator so we have one 9 in the denominator9This can then be cancelled down to be 3

16. ..0.12

17. ..0.12 12

18. ..0.122 digits 12

19. ..0.122 digits99 12

20. ..0.1234

21. ..0.1234 1234

22. ..0.1234 12344 digits

23. ..0.1234 12344 digits9999

24. ..0.1234 12344 digits9999

25. ..0.122 digits99 12..0.1234 12344 digits9999

26. ..0.122 digits99 12..0.1234 12344 digits9999

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

28. Now try theseWrite the following using the dot notation then convert them into exact fractions.0.111111111….0.4343434343 ….0.765765765 ….0.237823782378237….0.10.430.7650.2378......

29. Now try theseWrite the following using the dot notation then convert them into exact fractions.0.111111111….0.4343434343 ….0.765765765 ….0.237823782378237….0.10.430.7650.2378.... 1 43 99765 2378999..9 9999