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terminating decimal

This topic has 3 expert replies and 8 member replies
fruti_yum Master | Next Rank: 500 Posts Default Avatar
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terminating decimal

Post Wed Aug 05, 2009 1:32 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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


    anyone know any approaches to tackle this question?

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    GID09 Senior | Next Rank: 100 Posts Default Avatar
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    Post Wed Aug 05, 2009 1:59 pm
    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


    Above expression could be written as d = 1/ 10(2x5)^3 x 5^4. Hence there will be 3 zeros and 3 non zeros i.e d=1/625000. IMO C.

    fruti_yum Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Aug 05, 2009 2:14 pm
    GID09 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


    Above expression could be written as d = 1/ 10(2x5)^3 x 5^4. Hence there will be 3 zeros and 3 non zeros i.e d=1/625000. IMO C.
    No not right!

    GID09 Senior | Next Rank: 100 Posts Default Avatar
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    Post Wed Aug 05, 2009 3:31 pm
    I stand corrected, 1/625000 is 0.000016..so its 2.

    PussInBoots Master | Next Rank: 500 Posts
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    Post Wed Aug 05, 2009 4:32 pm
    1/(2^3 * 5^7) = 1/8 * 1/ 5^7 = .125 / 125 * 1/5^4 = .001 * .2 * .2 *.2 * .2 = .000...016

    aspiregmat Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Aug 06, 2009 2:31 am
    d = 1/(2^3 * 5^ 7)

    If a number is divided or multiplied by a power of 10 it will only change the decimal by inserting a 0 at appropriate place..

    In this case 2^3 and 5^3 will yield 1000 so questions reduces to

    d = 1/(5^4)

    now if we multiply denominator by 16 it yields again a number which is a power of 10.

    so question reduces to d = 16

    so answer is 2 i.e B

    fruti_yum Master | Next Rank: 500 Posts Default Avatar
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    Post Thu Aug 06, 2009 3:22 pm
    aspiregmat wrote:
    d = 1/(2^3 * 5^ 7)

    If a number is divided or multiplied by a power of 10 it will only change the decimal by inserting a 0 at appropriate place..

    In this case 2^3 and 5^3 will yield 1000 so questions reduces to

    d = 1/(5^4)

    now if we multiply denominator by 16 it yields again a number which is a power of 10.

    so question reduces to d = 16

    so answer is 2 i.e B
    any more solutions??

    shahdevine Master | Next Rank: 500 Posts Default Avatar
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    Post Thu Aug 06, 2009 4:48 pm
    fruti_yum 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


    anyone know any approaches to tackle this question?
    hey fruti,


    as far as tackling this type of problem...the gmat expects you to recognize 1/n where n=1 to 9...this is something you can choose to memorize. in this case we have 1/8 which is .125. Then if you isolate 1/n where n equals 5 to various powers a pattern emerges very quickly:

    1/5=.2 or 2 x 10^-1
    1/25=.04 or 4 x10^-2
    1/125=.008 or 8 x 10^-3
    etc
    you can intuit that 1/5^7 will be will have will be 128 x 10^-7....you can ignore the powers of 10. and multiply 128 by .125 and you will get a 2 digit number, 16. --->therefore b.

    again the approach for problem like this is pattern recognition based on powers of a number and dividing into 1. its somewhat tedious. but its worth it if you are shooting for 700+.

    you got this!

    tohellandback Legendary Member Default Avatar
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    Post Thu Aug 06, 2009 6:11 pm
    fruti_yum 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


    anyone know any approaches to tackle this question?
    1/(2^3*5^7)= 1/(1000)*625
    =1000/(1000)(1000)(625)

    1000/625=1.6
    answer 2
    B

    _________________
    The powers of two are bloody impolite!!

    Post Thu Aug 24, 2017 12:36 pm
    fruti_yum wrote:
    If d = 1/(2^3 x 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
    First let's examine the denominator
    We have: (2^3)(5^7)

    Notice that we can combine some 2's and 5's here.
    (5^7)(2^3) = (5^4)(5^3)(2^3)
    = (5^4)(10^3)
    So, d = 1/(5^4)(10^3)


    IMPORTANT: We can create an equivalent fraction, by multiplying top and bottom by the same value.
    So, to create some MORE 10's in the denominator, let's multiply top and bottom by 2^4
    When we do this, we get: d = (2^4)/(2^4)(5^4)(10^3)
    Simplify: d = (2^4)/(10^4)(10^3)
    Simplify more: d = (16)/(10^7)
    Rewrite as: d = 16/10,000,000
    Or as: d = 0.0000016

    So, d will have 2 non-zero digits when expressed as a decimal.

    Answer: B

    Cheers,
    Brent

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    Post Wed Aug 30, 2017 5:48 pm
    1/(2³5⁷) =>

    1/(2³5³5⁴) =>

    1/10³ * 1/5⁴ =>

    1/1000 * 1/25 * 1/25 =>

    .001 * .04 * .04

    The result will have as many decimal places as everything we're multiplying together, or 3 + 2 + 2 decimal places, or 7. Since 1 * 4 * 4 = 16, and those numbers come at the end, we're left with .0000016, or five leading zeros and two nonzero digits.

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    Post Mon Sep 04, 2017 10:30 am
    fruti_yum 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
    Since actually dividing 1/(2^3*5^7) would be time-consuming, we want to manipulate d so that we are working with a cleaner denominator. The easiest way to do that is to multiply d by a value that will produce a perfect power of 10 in the denominator. This means that the number of 2s in the denominator will equal the number of 5s in the denominator.

    Thus, we can multiply 1/(2^3*5^7) by 2^4/2^4. This gives us:

    2^4/(2^7*5^7)

    2^4/10^7

    16/10^7

    16/10,000,000

    We can stop here because we know that the 10,000,000 in the denominator means to move the decimal point after the 16 seven places to the left. The final value of d will be 0.0000016. (Note that the division of 16 by 10,000,000 did not produce any additional nonzero digits, and in general, for any positive integers a and n, a/10^n has the same number of nonzero digits as a.) Thus, d has 2 nonzero digits.

    Answer: B

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