GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 May 2019, 10:10

### 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

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

Author Message
Manager
Joined: 09 Sep 2004
Posts: 54
If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

Updated on: 17 Jun 2013, 22:47
1
12
00:00

Difficulty:

65% (hard)

Question Stats:

55% (00:58) correct 45% (00:59) wrong based on 308 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-d-1-2-3-5-7-is-expressed-as-a-terminating-decimal-how-144440.html

Originally posted by mba4me on 12 Sep 2004, 01:40.
Last edited by Bunuel on 17 Jun 2013, 22:47, edited 1 time in total.
Edited the question.
Director
Joined: 16 Jun 2004
Posts: 850

### Show Tags

12 Sep 2004, 11:13
1
I can only think of the following method...may not be most efficient

Step 1: Looking at the denominator = no. of two's and 5's will get as many 10's (we have three 2's and three 5's(amonf seven 5's) , so I will rewrite it as

(1000)*5^4

=> d= 0.001*1/(5^4)

step 2: I will rewrite 1/(5^4) as = (2/10)*(2/10)*(2/10)*(2/10) => 16*(1/10000)

step 3: We now have d =0.0000016.
So, 2 non zero digits.
Director
Joined: 20 Jul 2004
Posts: 563

### Show Tags

12 Sep 2004, 15:49
1
d = 1 / (2^3 x 5^7)
= 1 / (1000 x 5^4)
= 10^-3 x (1/625)
= 10^-7 x (10000/625)
= 10^-7 x 16

So 2 digits
Intern
Joined: 07 Feb 2013
Posts: 12
GMAT 1: 650 Q48 V32
GMAT 2: 730 Q49 V41
WE: Engineering (Other)
Re: If d = 1/(2^3*5^7) is expressed as a terminating decimal,  [#permalink]

### Show Tags

17 Jun 2013, 22:09
4
Another way to do it is :

We know x^a*y^a=(X*Y)^a

given = 1/(2^3*5^7)
= Multiply and divide by 2^4
=2^4/(2^3*2^4*5^7)
=2^4/10^7
=> non zero digits are 16 => Ans B
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

17 Jun 2013, 22:48
12
10
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-d-1-2-3-5-7-is-expressed-as-a-terminating-decimal-how-144440.html
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 11004
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

18 Aug 2018, 12:41
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.
_________________
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how   [#permalink] 18 Aug 2018, 12:41
Display posts from previous: Sort by