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

Kudos [?]: 1972  , given: 397

If 1/2^11*5^17 is expressed as a terminating decimal, how ma [#permalink]
1
KUDOS
Expert's post 00:00

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

Kudos [?]: 1972 , given: 397

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

Sandy
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GRE Instructor Joined: 10 Apr 2015
Posts: 2175
Followers: 64

Kudos [?]: 1986 , given: 20

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

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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