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

Question

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

Bunuel · Accepted Answer

Official Solution:

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

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

NavenRk · Answer

\frac{81}{125*10^3} = \frac{0.648}{10^3}

Hence answer is C

aj13783 · Answer

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

Zhenek · Answer

\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

htridn · Answer

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.

D3N0 · Answer

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

hsbinfy · Answer

C-three

81/(125∗10^3)=0.648/10^3

Hence answer is C

23a2012 · Answer

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

akhilbajaj · Answer

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.

vijayshree · Answer

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

PerseveranceWins · Answer

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.

shinrai15 · Answer

@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

Bunuel · Answer

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.

Rajeet123 · Answer

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?

sajibmannan · Answer

Multiplying the numerator and the denominator by 2^3 does not bring any changes to the original equation; it also helps us perform calculations to solve it.

Concept:

Exponents

Operations involving the same exponents: Keep the exponent, multiply or divide the bases. 
  a^n*b^n=(ab)^n

>  \frac{3^4}{2^3*5^6}*\frac{2^3}{2^3}

>  \frac{3^4*2^3}{2^6*5^6}

>  \frac{3^4*2^3}{10^6}

>  \frac{81*8}{10^6}

Multiplying the denominator by  2^3  helps convert it into a base of 10. This means we only need to focus on the numerator to find the non-zero digits. Since the numerator is smaller than the denominator, the result will be less than 1, with zeroes to the right of the decimal point. The non-zero digits will appear at the end. This approach makes it easier to identify the non-zero digits.

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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