How many positive integers less than 100 have reciprocals with terminating decimal res? (1) 13 (2) 14 (3) 21 (4) 25?
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Please find below the solution to the asked query:
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 ( Ans )
Hope this information will clear your doubts about topic.
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 ( Ans )
Hope this information will clear your doubts about topic.
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