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Recurring Decimals

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Recurring Decimals

1. 1. Recurring decimals<br />BTEOTSSBAT:<br /><ul><li>Write recurring decimals using the dot notation
2. 2. Change recurring decimals into exact fractions</li></li></ul><li>Key terms<br />Decimals<br />Fractions<br />Recurring<br />Exact<br />
3. 3. Recurring decimals<br />= 0.3333333333333……<br />3<br /> 1<br />
4. 4. Recurring decimals<br />… it keeps going on, it will never stop – we say it recurs.<br />= 0.3333333333333……<br />3<br /> 1<br />
5. 5. Recurring decimals<br />… it keeps going on, it will never stop – we say it recurs.<br />= 0.3333333333333……<br />3<br />We can write it in mathematical shorthand as:<br /> 1<br />
6. 6. Recurring decimals<br />… it keeps going on, it will never stop – we say it recurs.<br />= 0.3333333333333……<br />3<br />We can write it in mathematical shorthand as:<br /> 1<br />.<br />0.3333333333333…… = 0.3<br />
7. 7. 0.12121212121212… Is another recurring decimal<br />
8. 8. 0.12121212121212… Is another recurring decimal<br />This can be written as 0.12<br />.<br />.<br />
9. 9. 0.12121212121212… Is another recurring decimal<br />This can be written as 0.12<br />.<br />.<br />In the same way <br />0.12341234123412341234 =<br />
10. 10. 0.12121212121212… Is another recurring decimal<br />This can be written as 0.12<br />.<br />.<br />In the same way <br />0.12341234123412341234 =<br />.<br />.<br />0.1234<br />
11. 11. Recurring decimals as exact fractions<br />Recurring decimals can easily be written as fractions.<br />To do this:<br /><ul><li> place the recurring numbers at the top of the decimal (as the numerator)
12. 12. write as many 9s as there are digits in the numerator as the bottom bit (denominator)</li></li></ul><li>Recurring decimals as exact fractions<br />For example <br />Write 0.3 as an exact decimal <br />
13. 13. Recurring decimals as exact fractions<br />For example <br />Write 0.3 as an exact decimal <br />Here only one 3 is recurring <br />So the numerator is 3 <br /> 3<br />
14. 14. Recurring decimals as exact fractions<br />For example <br />Write 0.3 as an exact decimal <br />Here only one 3 is recurring <br />So the numerator is 3 <br /> 3<br /> 3<br />There is one digit in the numerator so we have one 9 in the denominator<br />9<br />
15. 15. Recurring decimals as exact fractions<br />For example <br />Write 0.3 as an exact decimal <br />Here only one 3 is recurring <br />So the numerator is 3 <br /> 3<br /> 3<br /> 1<br />There is one digit in the numerator so we have one 9 in the denominator<br />9<br />This can then be cancelled down to be <br />3<br />
16. 16. .<br />.<br />0.12<br />
17. 17. .<br />.<br />0.12<br /> 12<br />
18. 18. .<br />.<br />0.12<br />2 digits<br /> 12<br />
19. 19. .<br />.<br />0.12<br />2 digits<br />99<br /> 12<br />
20. 20. .<br />.<br />0.1234<br />
21. 21. .<br />.<br />0.1234<br /> 1234<br />
22. 22. .<br />.<br />0.1234<br /> 1234<br />4 digits<br />
23. 23. .<br />.<br />0.1234<br /> 1234<br />4 digits<br />9999<br />
24. 24. .<br />.<br />0.1234<br /> 1234<br />4 digits<br />9999<br />
25. 25. .<br />.<br />0.12<br />2 digits<br />99<br /> 12<br />.<br />.<br />0.1234<br /> 1234<br />4 digits<br />9999<br />
26. 26. .<br />.<br />0.12<br />2 digits<br />99<br /> 12<br />.<br />.<br />0.1234<br /> 1234<br />4 digits<br />9999<br />
27. 27. Now try these<br />Write the following using the dot notation then convert them into exact fractions.<br />0.111111111….<br />0.4343434343 ….<br />0.765765765 ….<br />0.237823782378237…<br />
28. 28. Now try these<br />Write the following using the dot notation then convert them into exact fractions.<br />0.111111111….<br />0.4343434343 ….<br />0.765765765 ….<br />0.237823782378237…<br />.<br />0.1<br />0.43<br />0.765<br />0.2378<br />.<br />.<br />.<br />.<br />.<br />.<br />
29. 29. Now try these<br />Write the following using the dot notation then convert them into exact fractions.<br />0.111111111….<br />0.4343434343 ….<br />0.765765765 ….<br />0.237823782378237…<br />.<br />0.1<br />0.43<br />0.765<br />0.2378<br />.<br />.<br />.<br />.<br /> 1<br /> 43<br /> 99<br />765<br /> 2378<br />999<br />.<br />.<br />9<br /> 9999<br />