Latest CAT Aptitude Question SOLUTION: Find number of zeros after decimal point in (5/6)^40? (Explanation requested)

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(#M40019660) CAT question Keep an EYE

Find number of zeros after decimal point in (5/6)^40?
(Explanation requested)

Asked In CAT Ramita Verma (10 years ago)

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Abhishek Mohanty  (7 years ago)

(5/6)^40

let us find the remainder first i.e:

(-1)^40 = 1

hence (5/6)^40 can be written as (6^40)*m + 1 where m is any positive integer

so the remainder will create the decimal structure hence the number after decimal will be 1/(6^40)

now the number of digits in 6^40 is = floor(1+log(6^40))=32

now when 1 is divided by a 32 digit number it will have 31 zeroes after decimal point for example....

1/2=0.5-----------0 zero
1/22=0.04---------1 zero
1/222=0.004-------2 zeroes

hence when 1/(32 digits)---------------31 zeroes

hence the ANS-------31

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