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Which of the following fractions will terminate when express

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Which of the following fractions will terminate when express  [#permalink]

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New post 25 Jan 2014, 18:03
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Which of the following fractions will terminate when expressed as a decimal?

(A) 1/259

(B) 27/101

(C) 100/27

(D) 231/660

(E) 1/11

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Which of the following fractions will terminate when express  [#permalink]

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New post 26 Jan 2014, 02:58
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rango wrote:
Which of the following fractions will terminate when expressed as a decimal?

(A) 1/259

(B) 27/101

(C) 100/27

(D) 231/660

(E) 1/11


THEORY:
Reduced fraction \(\frac{a}{b}\) (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only \(b\) (denominator) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as \(250\) (denominator) equals to \(2*5^3\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\).

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced.

BACK TO THE QUESTION:

If you check each option you get that only 231/660 will terminate: 231/660 = 7/20 = 7/(2^2*5).

Answer: D.

Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html

Hope it helps.
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Re: Which of the following fractions will terminate when express  [#permalink]

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New post 07 Aug 2014, 01:06
\(\frac{231}{660} = \frac{21}{60} = \frac{7}{20} = \frac{35}{100} = 0.35\)

No other option can be simplified further to bring \(10^n\) in the denominator

Answer = D
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Re: Which of the following fractions will terminate when express  [#permalink]

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New post 07 Sep 2018, 16:25
rango wrote:
Which of the following fractions will terminate when expressed as a decimal?

(A) 1/259

(B) 27/101

(C) 100/27

(D) 231/660

(E) 1/11


A fraction will convert to a terminating decimal when the denominator of the simplified fraction contains only 5’s, only 2’s, or both 5’s and 2’s.

Since 231/660 = 77/220 = 7/20, and the denominator 20 = 2^2 x 5, we see that 231/660 will terminate.

Answer: D
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Re: Which of the following fractions will terminate when express &nbs [#permalink] 07 Sep 2018, 16:25
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