Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 06 Jun 2020, 00:55 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64316
If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

4
37 00:00

Difficulty:   35% (medium)

Question Stats: 67% (01:32) correct 33% (01:52) wrong based on 543 sessions

### HideShow timer Statistics

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.

_________________
Manager  Joined: 17 Mar 2015
Posts: 113
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

24
9
$$\frac{3^4}{2^3*5^6}$$ = $$\frac{3^4*2^3}{2^6*5^6}$$ = $$\frac{81*8}{2^6*5^6}$$ =
$$\frac{648}{10^6}$$, which means that its gonna be 3 digits.

C
##### General Discussion
Intern  Joined: 01 Jan 2015
Posts: 17
If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

1
1
2
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.

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

Intern  Joined: 22 Aug 2014
Posts: 37
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

2
1
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
Intern  Joined: 22 Mar 2015
Posts: 3
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

1
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.
Current Student G
Joined: 21 Jan 2015
Posts: 451
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35 WE: Sales (Consumer Products)
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

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
_________________
--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Senior Manager  Joined: 02 Mar 2012
Posts: 258
Schools: Schulich '16
If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

1
C-three

81/(125∗10^3)=0.648/10^3

Manager  Status: Kitchener
Joined: 03 Oct 2013
Posts: 86
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

1
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
Director  G
Joined: 23 Jan 2013
Posts: 506
Schools: Cambridge'16
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

was stuck but it is clear that A and B out

guessed C
Manager  Joined: 09 Jan 2013
Posts: 60
Concentration: Entrepreneurship, Sustainability
GMAT 1: 650 Q45 V34
GMAT 2: 740 Q51 V39
GRE 1: Q790 V650
GPA: 3.76
WE: Other (Pharmaceuticals and Biotech)
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

2
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.

Intern  Joined: 09 Oct 2011
Posts: 20
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

1
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 .

Math Expert V
Joined: 02 Sep 2009
Posts: 64316
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

1
3
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 $$\frac{2^3}{2^3}$$:

$$\frac{3^4}{2^3*5^6}*\frac{2^3}{2^3}=\frac{3^4*2^3}{2^6*5^6}=\frac{81*8}{10^6}=\frac{648}{10^6}=0.000648$$.

_________________
Manager  B
Joined: 23 Apr 2014
Posts: 57
Location: United States
GMAT 1: 680 Q50 V31
GPA: 2.75
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

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.
Intern  B
Joined: 08 Sep 2016
Posts: 31
If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

@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?

S
Math Expert V
Joined: 02 Sep 2009
Posts: 64316
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

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?

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.
_________________
Manager  B
Joined: 15 Aug 2017
Posts: 68
Location: India
Schools: HBS '22
Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze  [#permalink]

### Show Tags

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?
_________________
"You don't want to to look back and know you could've done better". Re: If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze   [#permalink] 04 Aug 2019, 05:39

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