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Question

Express 15.7¯¯¯¯¯¯12 as a fraction in the simplest form.

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Solution

Let x=15.7¯¯¯¯¯¯12
i.e. x=15.7121212...(1)
Multiplying (1) by 10 and 100 successively, we get
10x=157.121212...(2)
and 1000x=15712.1212...(3)
Subtracting (2) from (3), we get
1000x10x=(15712.1212...)(157.1212...)
990x=15555
x=15555990
x=103766
Hence, 15.7¯¯¯¯¯¯12=103766

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