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If 1/2^11*5^17 is expressed as a terminating decimal, how ma

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1965 [1] , given: 397

If 1/2^11*5^17 is expressed as a terminating decimal, how ma [#permalink] New post 18 Jan 2016, 01:36
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Question Stats:

40% (00:11) correct 60% (00:44) wrong based on 30 sessions
If \(\frac{1}{(2^{11})(5^{17})}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?

A One
B Two
C Four
D Six
E Eleven


Practice Questions
Question: 16
Page: 333
Difficulty: hard
[Reveal] Spoiler: OA

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GRE Prep Club Legend
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User avatar
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1965 [0], given: 397

Re: expressed as a terminating decimal, how many nonzero digits [#permalink] New post 18 Jan 2016, 04:01
Expert's post
Solution

To convert the fraction to a decimal, it is helpful to first write the fraction in powers of 10.

\(\frac{1}{2^1^1*5^1^7}\)= \(\frac{1}{2^1^1*5^1^1*5^6}\)

Hence \(\frac{1}{5^6}*10^-^1^1\)= \(0.2^6 *10^-^1^1\)

or \(2^6 * 10 ^ - ^6* 10^-^1^1\)= \(64* 10 ^- ^1 ^7\).

Hence it has two non zero digits 6 and 4.
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Kudos [?]: 1975 [0], given: 19

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Re: expressed as a terminating decimal, how many nonzero digits [#permalink] New post 10 May 2019, 09:13
Expert's post
sandy wrote:
If \(\frac{1}{(2^{11})(5^{17})}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?

A One
B Two
C Four
D Six
E Eleven


Practice Questions
Question: 16
Page: 333
Difficulty: hard


\(\frac{1}{(2^{11})(5^{17})}=\frac{1}{(2^{-6})(2^{17})(5^{17})}\)

\(=\frac{1}{(2^{-6})(10^{17})}\)

\(=(\frac{1}{2^{-6}})(\frac{1}{10^{17}})\)

\(=(2^6)(\frac{1}{10^{17}})\)

\(=(64)(\frac{1}{10^{17}})\)

\(=\frac{64}{100,000,000,000,000,000}\)

\(= 0.00000.....064\)

There are 2 non-zero digits

Answer: B

Cheers,
Brent
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Re: expressed as a terminating decimal, how many nonzero digits   [#permalink] 10 May 2019, 09:13
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