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expressed as a terminating decimal, how many nonzero digits

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 111

Kudos [?]: 1851 [1] , given: 397

expressed as a terminating decimal, how many nonzero digits [#permalink]  18 Jan 2016, 01:36
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Expert's post
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Question Stats:

41% (00:11) correct 58% (00:47) wrong based on 29 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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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 111

Kudos [?]: 1851 [0], given: 397

Re: expressed as a terminating decimal, how many nonzero digits [#permalink]  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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Sandy
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GRE Instructor
Joined: 10 Apr 2015
Posts: 1743
Followers: 58

Kudos [?]: 1660 [0], given: 8

Re: expressed as a terminating decimal, how many nonzero digits [#permalink]  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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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