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If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze

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Bunuel
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If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze [#permalink] New post   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

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C
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Zhenek
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze [#permalink] New post   13 May 2015, 05:15
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\(\frac{3^4}{2^3*5^6}\) = \(\frac{3^4*2^3}{2^6*5^6}\) = \(\frac{81*8}{2^6*5^6}\) =
\(\frac{648}{10^6}\), which means that its gonna be 3 digits.

C
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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze [#permalink] New post   18 May 2015, 06:57
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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:

To transform the denominator into a base 10 format, which subsequently enables us to convert the fraction into a decimal of the form 0.xxxx, we should multiply the fraction \(\frac{3^4}{2^3*5^6}\) 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 [#permalink] New post   13 May 2015, 05:05
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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 [#permalink] New post   13 May 2015, 05:11
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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 non-zero 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 [#permalink] New post   13 May 2015, 20:01
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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 [#permalink] New post   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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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze [#permalink] New post   14 May 2015, 08:42
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C-three

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 [#permalink] New post   15 May 2015, 17:50
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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 [#permalink] New post   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 [#permalink] New post   16 May 2015, 01:05
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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 [#permalink] New post   16 May 2015, 01:49
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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 [#permalink] New post   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 non-zero value of final answer
So 3^4/(2^3*5^6) = 10^-3 * (81/125)
This final division gives us 3 non-zero digits.

In questions which asks us to find such non-zero 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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Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze [#permalink] New post   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 [#permalink] New post   20 Oct 2017, 07:12
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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 [#permalink] New post   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 [#permalink] New post   20 Jul 2023, 07:21
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