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# If d=1/(2^3*5^7) is expressed as a terminating decimal, how

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If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  20 Dec 2012, 05:11
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If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten
[Reveal] Spoiler: OA
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  20 Dec 2012, 05:12
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If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: d=\frac{1}{2^3*5^7}.

Multiply by \frac{2^4}{2^4} --> d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016. Hence d will have two non-zero digits, 16, when expressed as a decimal.

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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  14 Aug 2013, 01:10
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Bumping for review and further discussion.
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  17 Aug 2013, 18:02
Bunuel wrote:
Bumping for review and further discussion.

Bunuel I actually, do have question.

The expression is equal to 1/(2*5)^3(5^4)=1/625,000. Knowing this expression alone. Is there a way to figure out the answer? Just didn't occur to me to multiply by 2^4
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  12 Oct 2013, 09:18
Any similar questions like this that we can practice?

Also, in the denominator, why would we also not multiply 2^4 with 5^7?

Thanks,
C
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  21 Oct 2013, 00:59
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: d=\frac{1}{2^3*5^7}.

Multiply by \frac{2^4}{2^4} --> d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016. Hence d will have two non-zero digits, 16, when expressed as a decimal.

Is there any other method to do it . I mean it is difficult to think of 2^4 there and then .

Regards
Divyanshu
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  24 Oct 2013, 02:15
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  24 Oct 2013, 02:28
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Puneethrao wrote:
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!

Unfortunately this is not correct:

2^{-3}=\frac{1}{8}=0.125 not 0.002, which is 2/10^3 and 5^{-7}=\frac{1}{78,125}=0.0000128 not 0.0000007, which is 7/10^7.

Hope it helps.
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  24 Oct 2013, 02:53
Bunuel wrote:
Puneethrao wrote:
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!

Unfortunately this is not correct:

2^{-3}=\frac{1}{8}=0.125 not 0.002, which is 2/10^3 and 5^{-7}=\frac{1}{78,125}=0.0000128 not 0.0000007, which is 7/10^7.

Hope it helps.

Thanks a lot!! I don't know what i was thinking , such a stupid mistake!! Thanks once again!
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  29 Dec 2013, 11:57
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: d=\frac{1}{2^3*5^7}.

Multiply by \frac{2^4}{2^4} --> d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016. Hence d will have two non-zero digits, 16, when expressed as a decimal.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  29 Dec 2013, 12:00
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theGame001 wrote:
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: d=\frac{1}{2^3*5^7}.

Multiply by \frac{2^4}{2^4} --> d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016. Hence d will have two non-zero digits, 16, when expressed as a decimal.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks

Frankly, the red part does not make any sense...

The denominator is 2^7*5^7. Multiply it by 2^4. What do you get?
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  29 Dec 2013, 12:08
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Okay, I was getting confused with a(a+b) with a(a*b). Please excuse for the pointless question.
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  11 Mar 2014, 15:54
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: d=\frac{1}{2^3*5^7}.

Multiply by \frac{2^4}{2^4} --> d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016. Hence d will have two non-zero digits, 16, when expressed as a decimal.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  11 Mar 2014, 22:36
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WinterIsComing wrote:
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: d=\frac{1}{2^3*5^7}.

Multiply by \frac{2^4}{2^4} --> d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016. Hence d will have two non-zero digits, 16, when expressed as a decimal.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.

We need to multiply by 2^6/2^6 in order to convert the denominator to the base of 10 and then to convert the fraction into the decimal form: 0.xxxx.

Similar questions to practice:
if-t-1-2-9-5-3-is-expressed-as-a-terminating-decimal-ho-129447.html
if-d-1-2-3-5-7-is-expressed-as-a-terminating-decimal-128457.html

Hope this helps.
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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]  27 May 2014, 02:29
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Another approach:

\frac{1}{(2^3*5^7)} =\frac{1}{(2^3*5^3*5^4)} by splitting denominator.

= \frac{1}{(10^3*5^4)} = \frac{10^{-3}}{5^4}

Representing numerator as\frac{(10^4*10^{-7})}{5^4} = 2^4*10^{-7} = 16*10^{-7}

=.0000016 , Hence 2 digits.

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how   [#permalink] 27 May 2014, 02:29
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