Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Oct 2016, 07:57

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If d=1/(2^3*5^7) is expressed as a terminating decimal, how

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 4

Kudos [?]: 2095 [0], given: 0

If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

20 Dec 2012, 06:11
39
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

57% (02:12) correct 43% (01:30) wrong based on 1029 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35273
Followers: 6636

Kudos [?]: 85533 [21] , given: 10237

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

20 Dec 2012, 06:12
21
KUDOS
Expert's post
24
This post was
BOOKMARKED
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

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35273
Followers: 6636

Kudos [?]: 85533 [2] , given: 10237

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

14 Aug 2013, 02:10
2
KUDOS
Expert's post
Bumping for review and further discussion.
_________________
Manager
Joined: 12 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 48 [0], given: 28

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

17 Aug 2013, 19:02
Bunuel wrote:
Bumping for review and further discussion.

Bunuel I actually, do have question.

The expression is equal to 1/(2*5)^3(5^4)=1/625,000. Knowing this expression alone. Is there a way to figure out the answer? Just didn't occur to me to multiply by 2^4
Intern
Joined: 09 Sep 2013
Posts: 19
Followers: 1

Kudos [?]: 1 [0], given: 7

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

12 Oct 2013, 10:18
Any similar questions like this that we can practice?

Also, in the denominator, why would we also not multiply 2^4 with 5^7?

Thanks,
C
Intern
Joined: 02 Oct 2013
Posts: 12
Followers: 0

Kudos [?]: 3 [0], given: 1

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

21 Oct 2013, 01:59
Bunuel 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

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

Is there any other method to do it . I mean it is difficult to think of 2^4 there and then .

Regards
Divyanshu
Intern
Joined: 19 Oct 2013
Posts: 10
Location: United States
Concentration: Finance, Technology
GMAT Date: 11-06-2013
GPA: 3.5
WE: Engineering (Investment Banking)
Followers: 0

Kudos [?]: 7 [0], given: 13

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

24 Oct 2013, 03:15
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!
Math Expert
Joined: 02 Sep 2009
Posts: 35273
Followers: 6636

Kudos [?]: 85533 [3] , given: 10237

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

24 Oct 2013, 03:28
3
KUDOS
Expert's post
Puneethrao wrote:
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!

Unfortunately this is not correct:

$$2^{-3}=\frac{1}{8}=0.125$$ not 0.002, which is 2/10^3 and $$5^{-7}=\frac{1}{78,125}=0.0000128$$ not 0.0000007, which is 7/10^7.

Hope it helps.
_________________
Intern
Joined: 19 Oct 2013
Posts: 10
Location: United States
Concentration: Finance, Technology
GMAT Date: 11-06-2013
GPA: 3.5
WE: Engineering (Investment Banking)
Followers: 0

Kudos [?]: 7 [0], given: 13

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

24 Oct 2013, 03:53
Bunuel wrote:
Puneethrao wrote:
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!

Unfortunately this is not correct:

$$2^{-3}=\frac{1}{8}=0.125$$ not 0.002, which is 2/10^3 and $$5^{-7}=\frac{1}{78,125}=0.0000128$$ not 0.0000007, which is 7/10^7.

Hope it helps.

Thanks a lot!! I don't know what i was thinking , such a stupid mistake!! Thanks once again!
Manager
Joined: 13 Jul 2013
Posts: 75
GMAT 1: 570 Q46 V24
Followers: 0

Kudos [?]: 8 [0], given: 21

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

29 Dec 2013, 12:57
Bunuel 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

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 35273
Followers: 6636

Kudos [?]: 85533 [2] , given: 10237

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

29 Dec 2013, 13:00
2
KUDOS
Expert's post
theGame001 wrote:
Bunuel 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

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks

Frankly, the red part does not make any sense...

The denominator is $$2^7*5^7$$. Multiply it by $$2^4$$. What do you get?
_________________
Manager
Joined: 13 Jul 2013
Posts: 75
GMAT 1: 570 Q46 V24
Followers: 0

Kudos [?]: 8 [1] , given: 21

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

29 Dec 2013, 13:08
1
KUDOS
Okay, I was getting confused with a(a+b) with a(a*b). Please excuse for the pointless question.
Intern
Joined: 29 Jan 2014
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

11 Mar 2014, 16:54
Bunuel 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

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.
Math Expert
Joined: 02 Sep 2009
Posts: 35273
Followers: 6636

Kudos [?]: 85533 [1] , given: 10237

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

11 Mar 2014, 23:36
1
KUDOS
Expert's post
WinterIsComing wrote:
Bunuel 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

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.

We need to multiply by 2^6/2^6 in order to convert the denominator to the base of 10 and then to convert the fraction into the decimal form: 0.xxxx.

Similar questions to practice:
if-t-1-2-9-5-3-is-expressed-as-a-terminating-decimal-ho-129447.html
if-d-1-2-3-5-7-is-expressed-as-a-terminating-decimal-128457.html

Hope this helps.
_________________
Intern
Joined: 24 Aug 2013
Posts: 5
Followers: 0

Kudos [?]: 5 [1] , given: 9

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

27 May 2014, 03:29
1
KUDOS
Another approach:

$$\frac{1}{(2^3*5^7)}$$ =$$\frac{1}{(2^3*5^3*5^4)}$$ by splitting denominator.

= $$\frac{1}{(10^3*5^4)}$$ = $$\frac{10^{-3}}{5^4}$$

Representing numerator as$$\frac{(10^4*10^{-7})}{5^4}$$ = $$2^4*10^{-7}$$ = $$16*10^{-7}$$

=.0000016 , Hence 2 digits.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12210
Followers: 541

Kudos [?]: 151 [0], given: 0

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

05 Jun 2015, 13:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 31 Oct 2015
Posts: 37
Followers: 0

Kudos [?]: 2 [0], given: 53

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

05 Jan 2016, 07:03
2^7 * 1/(10^7) * 2^-3 = 2^4 * 1/(10^7) = 16/10000000 = .000000016

Senior Manager
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 296
Followers: 16

Kudos [?]: 77 [1] , given: 2

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

23 Jun 2016, 09:38
1
KUDOS
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 place 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 non-zero digits. Thus d has 2 non-zero digits.

_________________

Jeffrey Miller
Jeffrey Miller

Math Forum Moderator
Status: Quant & Verbal Forum Moderator
Joined: 11 Jun 2011
Posts: 1627
Location: India
GPA: 3.5
Followers: 57

Kudos [?]: 401 [1] , given: 271

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

23 Jun 2016, 11:35
1
KUDOS
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

$$d$$ = $$\frac{1}{(2^3*5^7)}$$

=>$$d$$ = $$\frac{1}{(2^3*5^3*5^4)}$$

=>$$d$$ = $$\frac{1}{(10^3*5^4)}$$

$$\frac{1}{5}$$ = $$0.20$$

$$\frac{1}{25}$$ = $$\frac{0.20}{5}$$ => $$0.04$$

$$\frac{1}{125}$$ = $$\frac{0.04}{5}$$ => $$0.008$$

$$\frac{1}{625}$$ = $$\frac{0.008}{5}$$ => $$0.0016$$

Hence there will be 2 non zero digits...

Feel free to revert in case of any doubt ( I have used some shortcuts , would love to explain if needed )

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum

Manager
Joined: 24 May 2014
Posts: 88
Location: India
GMAT 1: 590 Q39 V32
GRE 1: 310 Q159 V151
GRE 2: 312 Q159 V153
GPA: 2.9
Followers: 0

Kudos [?]: 6 [0], given: 316

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]

### Show Tags

12 Sep 2016, 08:11
I solved the question in the following method, not sure whether it is correct:

1/2^3 x 5^7 = 1/2^3 x 5^3 [Equating the power of 2 & 5 to get the number of zeros], left with 1/5^4 = 1/625 = 0.00105. Only 1 & 5 are the non-zero digits.
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how   [#permalink] 12 Sep 2016, 08:11

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
Which of the following can be expressed as a terminating decimal? 2 02 May 2016, 22:31
24 If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze 12 13 May 2015, 04:30
34 If 1/(2^11 * 5^17) is expressed as a terminating decimal, ho 7 27 Nov 2011, 19:34
4 If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma 5 15 Aug 2011, 15:24
5 If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero 4 23 Feb 2011, 08:52
Display posts from previous: Sort by