Wednesday, 21 September 2011

Recurring Nightmare

Recurring decimals are the current topic in my fifth year and they have been learning the method of converting them into fractions:

The basic idea is to let your recurring decimal be x, multiply by a power of 10 as necessary and then subtract to eliminate the recurring part:


eg if x = 0.7777777777777777.........

then 10x = 7.7777777777777777.......


subtracting the top one from the bottom gives us 9x = 7 and so,

dividing by 9, x = 7/9

hence 0.77777777777............ = 7/9


Simple?


Well, what about 0.999999999........?


If x = 0.9999999.........

10x = 9.9999999999..............


so 9x = 9 and x = 9/9=1

hence 0.99999999999......... = 1 !!!!

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