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When x/32 is expressed in decimal form

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When x/32 is expressed in decimal form [#permalink]

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New post 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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Re: When x/32 is expressed in decimal form [#permalink]

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New post 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.

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Re: When x/32 is expressed in decimal form [#permalink]

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New post 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: \(\frac{9}{30}=\frac{3*3}{3*5*2}=\frac{3}{10}\)

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Re: When x/32 is expressed in decimal form [#permalink]

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New post 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.

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Re: When x/32 is expressed in decimal form [#permalink]

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New post 27 Jul 2009, 12:43
Are there any universal rules regarding terminating decimals that are helpful?

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Re: When x/32 is expressed in decimal form [#permalink]

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New post 27 Jul 2009, 14:52
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If you want to know if a fraction represents a terminating decimal:

1. reduce your fraction completely
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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Re: When x/32 is expressed in decimal form [#permalink]

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

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Re: When x/32 is expressed in decimal form   [#permalink] 27 Jul 2009, 15:01
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