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If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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13 May 2015, 04:30
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If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have? A. One B. Two C. Three D. Four E. Six Kudos for a correct solution.
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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13 May 2015, 05:15
\(\frac{3^4}{2^3*5^6}\) = \(\frac{3^4*2^3}{2^6*5^6}\) = \(\frac{81*8}{2^6*5^6}\) = \(\frac{648}{10^6}\), which means that its gonna be 3 digits.
C




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If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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13 May 2015, 05:05
Bunuel wrote: If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One B. Two C. Three D. Four E. Six
Kudos for a correct solution. \(\frac{81}{125*10^3} = \frac{0.648}{10^3}\) Hence answer is C



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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13 May 2015, 05:11
Bunuel wrote: If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One B. Two C. Three D. Four E. Six
Kudos for a correct solution. We have to find the count of nonzero nos in the expression 3^4/2^3*5^6 If you look at the nos in denominator, we can see that it is 2 and 5. 2*5 = 10 and this will not divide the fraction and give new nos. Thus the eqn can be changed to = 3^4 /5^3 * 10^3 = 81/125 (10^3 is not required as it does not alter the solution) = 0.648 Thus, # non zero decimal nos is 3 Option C



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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13 May 2015, 20:01
3^4/(2^3*5^6) = 3^4/(2^3*5^3*5^3) = 3^4/(10^3*5^3) = 10^3 * 3^4/5^3 = 10^3 * 81/125 ==> 10^3 *0.625 ==> choose C.



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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13 May 2015, 22:09
Bunuel wrote: If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One B. Two C. Three D. Four E. Six
Ans: C Solution: given question has 3^4=81, 2^3*5^6= 10^3*5^3 now (81*10^3)/5^3 which gives us 648 if we remove the decimal part for now. as we know we need to find how many nonzero digits are there, three is the answer. ans: C
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If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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14 May 2015, 08:42
Cthree
81/(125∗10^3)=0.648/10^3
Hence answer is C



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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15 May 2015, 17:50
the answer is C we can multiple the numerator and denominator by 2^3 to get the powers of 2 and 5 in the denominator are equal so 3^4*2^3/2^6*5^6= 81*8/10^6 =648/10^6
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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15 May 2015, 22:06
was stuck but it is clear that A and B out
guessed C



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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16 May 2015, 01:05
Just convert the denominator into power of 10. You don't really need to do any calculation
\(\frac{3^4}{2^3*5^6} = \frac{3^4*2^3}{10^6} = \frac{81*8}{10^6}\)
81*8 is clearly a 3 digit no.
Answer C.



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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16 May 2015, 01:49
Let 's understand the concept of terminating decimal
terminating decimal = 1/ 2 power a * 1/ 5 power of b ( concept )
Now multiply by 2 to the power of 3 with Numerator and denominator to convert terminating decimal .
Now exponent concept  2to the power 6 and 5 to the power 6 = 10 to the power 6
Now original fraction became
648/ 1000000 = .000648
Hence After decimal there are 3 Non zeros .
Answer c



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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18 May 2015, 06:57
Bunuel wrote: If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One B. Two C. Three D. Four E. Six
Kudos for a correct solution. OFFICIAL SOLUTION:Multiply \(\frac{3^4}{2^3*5^6}\) by \(\frac{2^3}{2^3}\): \(\frac{3^4}{2^3*5^6}*\frac{2^3}{2^3}=\frac{3^4*2^3}{2^6*5^6}=\frac{81*8}{10^6}=\frac{648}{10^6}=0.000648\). Answer: C.
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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06 Dec 2016, 19:08
Bunuel wrote: If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One B. Two C. Three D. Four E. Six
Kudos for a correct solution. Denominator has powers of 2 and 5, so this gives hint that there is power of 10 actually in denominator. Segregating powers of 10 will help in final division. Denominator: 2^3 * 5^6 = (2^3 * 5^3) * 5^3 = 10^3 * 125 So final value is 81/1000*125 Now 1000 in denominator will not add to nonzero value of final answer So 3^4/(2^3*5^6) = 10^3 * (81/125) This final division gives us 3 nonzero digits. In questions which asks us to find such nonzero digits , we can simply segregate common powers of 2 and 5 from denominator as they lead to zeroes after division. Hope this helps.



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If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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20 Oct 2017, 07:03
@Bunnel,
This might be really basic but i am unable to understand why the numerator and denominator are multiplied by 2^3?
Please explain. what am i missing?
Thanks in Advance! S



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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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20 Oct 2017, 07:12
shinrai15 wrote: @Bunnel,
This might be really basic but i am unable to understand why the numerator and denominator are multiplied by 2^3?
Please explain. what am i missing?
Thanks in Advance! S We need to multiply by 2^3/2^3 in order to convert the denominator to the base of 10 and then to convert the fraction into the decimal form: 0.xxxx.
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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04 Aug 2019, 06:39
Bunuel wrote: If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One B. Two C. Three D. Four E. Six
Kudos for a correct solution. 10 can be created in the above equation by 2*5 only. Since we've only three 2's, we can create a max of three 10's. Hence 3 zeros. However, I'm not sure if this logic is right. Comments?
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze
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