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

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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, 04:16
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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 Updated on: 25 Aug 2019, 06:57
1/ab = 1/(6^5*5^6) = 1/(3^5*10^5*5)
= 1/1215 * 10^-5 = (1/1.215)*10^-8
(1/1.215) is a number less than 1 but greater than 0.1 of the form '0.xyz' where x,y,z are single digit numbers with x <> 0
This will give 8 zeros between decimal point and first non-zero digit right of the decimal point.

Answer is B


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Originally posted by karthik1488 on 11 Aug 2019, 05:07.
Last edited by karthik1488 on 25 Aug 2019, 06:57, edited 1 time in total.
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Re: For the positive integers a and b, represents the number of zeros bet  [#permalink]

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New post 24 Aug 2019, 15:45
2^5·3^5·5^6
Combine the 2s and 5s to get terminating 0s.
10^5·3^5·5=121,500,000

It is the reciprocal so 1/121,500,000

And I said 9 as there are nine digits. Calculator tells me 8. Don't know why. Expert please respond
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Re: For the positive integers a and b, represents the number of zeros bet   [#permalink] 24 Aug 2019, 15:45

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

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