Question

how many positive integers less than 100 reciprocal with terminating decimal representatives​

Answer 1

Answer:

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Answer 2

We know denominator of a fraction is in form of 2m × 5n .

We know : Number multiple of only 2 and less than 100 = 2 , 4 , 8 , 16 , 32 , 64 ( 6 numbers )

And

Number multiple of only 5 and less than 100 = 5 , 25 ( 2 numbers )

And

Number multiple of only 2 and 5 and less than 100 = 10 , 20 , 40 , 50 , 80 ( 5 numbers )

And we know reciprocal of 1 is 1 . so that also gives terminating decimal digits .

Therefore,

Total numbers that have reciprocal with terminating decimal digits = 6 + 2 + 5 + 1 = 14.

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