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# When x/32 is expressed in decimal form

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Director
Joined: 25 Oct 2008
Posts: 574
Location: Kolkata,India
When x/32 is expressed in decimal form [#permalink]

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17 Jul 2009, 02:34
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When x/32 is expressed in decimal form,it is a terminating decimal.Which of the following could be the value of x?
(1)3 (2)5 (3)8

[Reveal] Spoiler:
Ans:All three

Guys unfortunatly I don't understand the concept.Anybody care to explain?

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Senior Manager
Joined: 23 Jun 2009
Posts: 355
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: When x/32 is expressed in decimal form [#permalink]

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17 Jul 2009, 04:47
http://www.icoachmath.com/SiteMap/Termi ... cimal.html
Terminating decimal is a decimal that terminates in finite digits.
x/32=x. 1/32 = x. 0,03125. So for every value of x; x/32 is a terminating decimal.
Manager
Joined: 15 Apr 2008
Posts: 50
Location: Moscow
Re: When x/32 is expressed in decimal form [#permalink]

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17 Jul 2009, 06:50
tejal777 wrote:
Guys unfortunatly I don't understand the concept.Anybody care to explain?

What is a terminating decimal? It is a fraction, that can be written down in the form of $$\frac{x}{10} or \frac{x}{100} or \frac{x}{1000}, etc$$, in other words $$\frac{x}{10^y}$$, where x and y are integers. It means, that if the fraction is terminating, its simplified version can be written with only 5's or 2' in denominator. Please pay attention to the word "simplified", as a fraction can have other primes in denominator, if they are "cut" by the same primes in numerator: for example $$\frac{9}{30}$$ has 3's, 5's and 2's in denominator, but still it is a terminating decimal: $$\frac{9}{30}=\frac{3*3}{3*5*2}=\frac{3}{10}$$
Senior Manager
Joined: 18 Jun 2009
Posts: 351
Location: San Francisco
Re: When x/32 is expressed in decimal form [#permalink]

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17 Jul 2009, 09:45
A Terminating decimal is one which terminates unline 0.333333 or values of pi

In this case all the three values of x when substituted in x/32 have definite number of values after the decimal point and hence the answer is all three

Its easy but lengthy as 3/32 and 5/32 have more than 3 decimal places.
Manager
Joined: 21 Jul 2009
Posts: 238
Location: New York, NY
Re: When x/32 is expressed in decimal form [#permalink]

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27 Jul 2009, 12:43
Are there any universal rules regarding terminating decimals that are helpful?
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346
Re: When x/32 is expressed in decimal form [#permalink]

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27 Jul 2009, 14:52
1
KUDOS
Expert's post
If you want to know if a fraction represents a terminating decimal:

2. prime factorize the denominator. If the only prime divisors of the denominator are 2, 5, or both, the decimal will terminate. Otherwise it will not.

So 7/32 = 7/2^5 terminates, as does 11/40 = 11/(2^3)(5), and as does 8/125 = 8/5^3. On the other hand, 7/72 = 7/(2^3)(3^2) and 11/60 = 11/(2^2)(3)(5) are both repeating decimals, since they are reduced fractions, and a prime different from 2 or 5 divides the denominator.
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Senior Manager
Joined: 25 Mar 2009
Posts: 294
Re: When x/32 is expressed in decimal form [#permalink]

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27 Jul 2009, 15:01
IanStewart's posts are nuggets of gold. By the way, how do you happen to know all these tricks?

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: When x/32 is expressed in decimal form   [#permalink] 27 Jul 2009, 15:01
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