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For the positive integers a and b, represents the number of zeros bet

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Posts: 3454
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For the positive integers a and b, represents the number of zeros bet  [#permalink]

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New post 11 Aug 2019, 05:16
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For the positive integers \(a\) and \(b\), \(k'\) represents the number of zeros between the decimal point and the first nonzero digit to the right of the decimal point in the reciprocal of the product of \(a\) and \(b\), when that reciprocal is expressed as a terminating decimal. What is the value of \(k' (6^5, 5^6)\) ?

A. 7

B. 8

C. 9

D. 10

E. 11

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For the positive integers a and b, represents the number of zeros bet  [#permalink]

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New post 11 Aug 2019, 06:07
1/ab = 1/(6^5*5^6) = 1/(3^5*10^5*5)
= 1/1215 * 10^-5
1/1215 has three zeros between decimal point and first non zero digit.
10^-5 has four zeros between decimal point and first non zero digit.
So k' = 3 + 4 = 7


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For the positive integers a and b, represents the number of zeros bet   [#permalink] 11 Aug 2019, 06:07
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