If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 06:08

### 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 t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero

Author Message
TAGS:

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 42

Kudos [?]: 864 [0], given: 39

If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]

### Show Tags

23 Feb 2011, 07:52
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

54% (01:00) correct 46% (01:14) wrong based on 56 sessions

### HideShow timer Statistics

If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point?

a. three
b. four
c. five
d. six
c. nine
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1708 [4] , given: 376

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]

### Show Tags

23 Feb 2011, 08:12
4
KUDOS
$$t= \frac{1}{2^9 * 5^3}$$

$$t= \frac{1}{2^6 * 2^3 * 5^3}$$

$$t= \frac{1}{2^6 * (2*5)^3}$$

$$t= \frac{1}{64 * (10)^3}$$

Multiplying numerator and denominator by $$10^2$$

$$t= \frac{10^2}{64 * (10)^5}$$

$$t= \frac{1.something}{(10)^5}$$

$$t= 1.something * 10^{-5}$$

To remove $$10^{-5}$$ we need to move decimal point 5 digits to the left

$$t= .00001something$$

4 zeros between decimal and first non-zero digit.

Ans: "B"
_________________
Manager
Joined: 17 Feb 2011
Posts: 200
Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44
Followers: 44

Kudos [?]: 708 [0], given: 70

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]

### Show Tags

23 Feb 2011, 12:30
I think there is no easier way than this.

fluke wrote:
$$t= \frac{1}{2^9 * 5^3}$$

$$t= \frac{1}{2^6 * 2^3 * 5^3}$$

$$t= \frac{1}{2^6 * (2*5)^3}$$

$$t= \frac{1}{64 * (10)^3}$$

Multiplying numerator and denominator by $$10^2$$

$$t= \frac{10^2}{64 * (10)^5}$$

$$t= \frac{1.something}{(10)^5}$$

$$t= 1.something * 10^{-5}$$

To remove $$10^{-5}$$ we need to move decimal point 5 digits to the left

$$t= .00001something$$

4 zeros between decimal and first non-zero digit.

Ans: "B"
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 514 [0], given: 36

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]

### Show Tags

23 Feb 2011, 20:46
1/1000 * 1/2^6 = 5^6/5^6 * 1/2^6 * 1/1000 = 5^6/10^9 = 5 digits/10^9

=> Answer is B (4 zeroes)
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7131
Location: Pune, India
Followers: 2140

Kudos [?]: 13711 [1] , given: 222

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]

### Show Tags

30 Mar 2011, 18:52
1
KUDOS
Expert's post
What fluke did above is great. Let me just add here that if you are stuck with how to proceed, don't shy away from quick and easy calculations.

$$\frac{1}{2^9*5^3} = \frac{1}{2^6*1000}$$

Now, I can divide 1 by 64 to get the decimal point: .01

If I divide this further by 1000, the decimal moves 3 places to the left and I get four 0s before the 1.

Sometimes, under pressure in the exam, Math will fail you. Go with your instincts and use logic. (Except if your instincts tell you to multiply a four digit number with a five digit number - then you are definitely missing the point!)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 30 Jul 2011
Posts: 119
Location: United States (NJ)
Concentration: General Management, Finance
GMAT 1: 520 Q40 V21
GPA: 2.95
Followers: 2

Kudos [?]: 24 [0], given: 24

If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma [#permalink]

### Show Tags

15 Aug 2011, 14:24
2
This post was
BOOKMARKED
If $$t= 1/(2^9x5^3)$$ is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point?

(a) 3
(b) 4
(c) 5
(d) 6
(e) 9
Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 115 [1] , given: 42

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma [#permalink]

### Show Tags

15 Aug 2011, 15:22
1
KUDOS
given expression can be re written as

5^6/(2^9*5^3*5^6) = 5^6/10^9

15625/10^9

=> 4 zero's between the decimal point and the first non zero digit to the right of the decimal point.

Director
Joined: 03 May 2007
Posts: 886
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 190 [0], given: 7

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma [#permalink]

### Show Tags

15 Aug 2011, 17:25
This should be the approach. +1.

Spidy001 wrote:
given expression can be re written as

5^6/(2^9*5^3*5^6) = 5^6/10^9

15625/10^9

=> 4 zero's between the decimal point and the first non zero digit to the right of the decimal point.

If the question were only about the terminating decimal, I would solve as under:

t= 1/(2^9 * 5^3)
t= 1/(2^6 * 10^3)
t= (0.5)^6 * (0.1)^3

Since the sum of the powers of the two decimals is 9, the terminating decimal has 9 decimals.
Manager
Joined: 05 Oct 2011
Posts: 171
Followers: 9

Kudos [?]: 51 [1] , given: 62

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma [#permalink]

### Show Tags

02 Nov 2011, 11:57
1
KUDOS
You could also use bench mark values as MGmat strategy guide talks about.
so here
1/100,000 < 1/64,000 <1/10,000
which is
0.00001 < 1/64000< 0.0001

So, t can be a like 0.000011, 0.000012 etc
so there are four zeroes.

Takeaway is to use Benchmark values.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13539
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma [#permalink]

### Show Tags

28 Mar 2016, 04:07
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.
_________________
Senior Manager
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 472
Followers: 22

Kudos [?]: 198 [1] , given: 2

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how ma [#permalink]

### Show Tags

04 May 2016, 08:31
1
KUDOS
restore wrote:
If $$t= 1/(2^9x5^3)$$ is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point?

(a) 3
(b) 4
(c) 5
(d) 6
(e) 9

Solution:

We use the term "leading zeros" to describe the zeros between the decimal point and the first nonzero decimal digit. To complete this problem we can use the following rule to determine the number of leading zeros in a fraction when it is converted to a decimal:

If X is an integer with k digits, then 1/X will have k – 1 leading zeros unless X is a perfect power of 10, in which case there will be k – 2 leading zeros.

We see that t is in the form 1/X. Because the denominator X has more twos than fives, we know X is not a perfect power of 10. Before considering the fraction as a whole, we first must determine the number of digits in the denominator.

Rewriting the denominator, we get 2^9 x 5^3 = (2^6 x 2^3) x 5^3 = 2^6 x (2^3 x 5^3) = 64 x (1,000) = 64,000, which is a 5-digit integer. Thus, k = 5.

Using our rule, we see that the fraction t has 5 - 1 = 4 leading zeros.

_________________

Jeffrey Miller
Jeffrey Miller

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13539
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]

### Show Tags

07 Jan 2017, 00:59
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 t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero   [#permalink] 07 Jan 2017, 00:59
Similar topics Replies Last post
Similar
Topics:
How many zeros to the left of the decimal would the number 300! have? 4 19 Jan 2017, 07:03
1 Which of the following can be expressed as a terminating decimal? 2 02 May 2016, 21:31
3 How many leading zeros (zeros after the decimal point but before the 4 25 Apr 2016, 03:01
26 If 3^4/(2^3*5^6) is expressed as a terminating decimal, how many nonze 13 13 May 2015, 03:30
93 If d=1/(2^3*5^7) is expressed as a terminating decimal, how 20 20 Dec 2012, 05:11
Display posts from previous: Sort by