Author 
Message 
TAGS:

Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 545

If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
23 Feb 2011, 08:52
Question Stats:
53% (01:14) correct 47% (01:04) wrong based on 155 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 OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ift1295 ... 4720.html
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Collections: PSof OG solved by GC members: http://gmatclub.com/forum/collectionpswithsolutionfromgmatclub110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collectiondswithsolutionfromgmatclub110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmatprepproblemcollections114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collectionsofworkrateproblemwithsolutions118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixtureproblemswithbestandeasysolutionsalltogether124644.html



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1901

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
23 Feb 2011, 09:12
\(t= \frac{1}{2^9 * 5^3}\) \(t= \frac{1}{2^6 * 2^3 * 5^3}\) \(t= \frac{1}{2^6 * (2*5)^3}\) \(t= \frac{1}{64 * (10)^3}\) 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 nonzero digit. Ans: "B"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 17 Feb 2011
Posts: 156
Concentration: Real Estate, Finance
Schools: MIT (Sloan)  Class of 2014

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
23 Feb 2011, 13:30
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 nonzero digit.
Ans: "B"



Retired Moderator
Joined: 16 Nov 2010
Posts: 1472
Location: United States (IN)
Concentration: Strategy, Technology

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
23 Feb 2011, 21:46
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: 8100
Location: Pune, India

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
30 Mar 2011, 19:52
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: 106
Location: United States (NJ)
Concentration: General Management, Finance
GPA: 2.95

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
15 Aug 2011, 15:24
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: 686

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
15 Aug 2011, 16:22
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.
Answer is B.



Director
Joined: 03 May 2007
Posts: 834
Schools: University of Chicago, Wharton School

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
15 Aug 2011, 18:25
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.
Answer is B. 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: 165

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
02 Nov 2011, 12:57
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.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
04 May 2016, 09:31
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 5digit integer. Thus, k = 5. Using our rule, we see that the fraction t has 5  1 = 4 leading zeros. Answer B.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 21 May 2016
Posts: 23

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
18 Mar 2017, 06:44
Baten80 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. three b. four c. five d. six c. nine I like the explanation from Mike McGarry on Magoosh's site and I'm reposting the explanation here: t=1/(2^9*5^3) t=1/(10^3*2^6) Now multiply the numerator and denominator by 5^6 so that we can convert the denominator completely in powers of 10 t=5^6/(10^3*2^6*5^6) t=5^6/(10^9) Now 5^3=125, 5^6 = (125)^2. If (100)^2 = 10,000, then (125)^2 will also have 5 digits So fill in the gap in this 9 digit number with the last 5 digits being 125^2 t=_ _ _ _ X X X X X. The first four blanks will obviously have zeros filled



Math Expert
Joined: 02 Sep 2009
Posts: 46129

Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero [#permalink]
Show Tags
18 Mar 2017, 06:56
Baten80 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. three b. four c. five d. six c. nine Given: \(t=\frac{1}{2^9*5^3}\). Multiply by \(\frac{5^6}{5^6}\) > \(t=\frac{5^6}{(2^9*5^3)*5^6}=\frac{25*625}{10^9}=\frac{15625}{10^9}=0.000015625\). Hence \(t\) will have 4 zerose between the decimal point and the fist nonzero digit. Answer: B. Or another way \(t=\frac{1}{2^9*5^3}=\frac{1}{(2^3*5^3)*2^6}=\frac{1}{10^3*64}=\frac{1}{64000}\). Now, \(\frac{1}{64,000}\) is greater than \(\frac{1}{100,000}=0.00001\) and less than \(\frac{1}{10,000}=0.0001\), so \(\frac{1}{64,000}\) is something like \(0.0000xxxx\). Answer: B. OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ift1295 ... 4720.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: If t= 1/(2^9x5^3) is expressed as a terminating decimal, how many zero
[#permalink]
18 Mar 2017, 06:56






