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# Which of the following fractions

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Which of the following fractions [#permalink]  08 Jan 2010, 14:22
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33% (01:02) correct 66% (00:53) wrong based on 5 sessions
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128
[Reveal] Spoiler:
E

Can some one tell how to solve it in a faster way?
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Re: Which of the following fractions [#permalink]  08 Jan 2010, 14:59
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sagarsabnis wrote:
Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128
[Reveal] Spoiler:
E

Can some one tell how to solve it in a faster way?

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*5^2. Fraction \frac{3}{30} is also a terminating decimal, as \frac{3}{30}=\frac{1}{10} and denominator 10=2*5.

\frac{39}{128}=\frac{39}{2^7}, denominator has only prime factor 2 in its prime factorization, hence this fraction will be terminating decimal.

All other fractions (after reducing, if possible) have primes other than 2 and 5 in its prime factorization, hence they will be repeated decimals.

Hope it's clear.
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Re: terminal decimal? [#permalink]  12 Sep 2010, 08:57
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Merging similar topics.
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Re: Which of the following fractions [#permalink]  14 Sep 2010, 05:51
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prashantbacchewar wrote:
Hi Bunuel
As per your explanation if the denominator is not in the form of 2^n 5^m then the fraction will be terminal decimal. If you look at the denominator of other answer choices they are also not in the above form
1. 189 = 3^3 *7^1
2. 196 = 2^2 * 7^2
3. 225 = 3^2 * 5^2
4. 144 = 2^4 * 3^2

So how the last answer choice is correct still not clear based on your explanation?

As per solution:

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*5^2. Fraction \frac{3}{30} is also a terminating decimal, as \frac{3}{30}=\frac{1}{10} and denominator 10=2*5.

A. \frac{10}{189}=\frac{10}{3^3*7} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated decimal;

B. \frac{15}{196}=\frac{15}{2^2*7^2} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated decimal;

C. \frac{16}{225}=\frac{16}{3^2*5^2} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated decimal;

D. \frac{25}{144}=\frac{25}{2^4*3^2} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated decimal.

E. \frac{39}{128}=\frac{39}{2^7}, denominator has only prime factor 2 in its prime factorization, hence this fraction will be terminating decimal. All other fractions' denominator have primes other than 2 and 5 in its prime factorization, hence they WILL BE repeated decimals:

Hope it's clear.

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Re: Which of the following fractions [#permalink]  08 Jan 2010, 15:54
Excellent explanation buddy!!!!
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Re: Which of the following fractions [#permalink]  12 Jan 2010, 04:35
Bunuel:

numbers with terminating decimals basically should have 5 or 2 or both in its denominators, right? So any numerator with denominator 125 or 8 would be a terminating decimal?

Thanks.
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Re: Which of the following fractions [#permalink]  12 Jan 2010, 09:05
study wrote:
Bunuel:

numbers with terminating decimals basically should have 5 or 2 or both in its denominators, right? So any numerator with denominator 125 or 8 would be a terminating decimal?

Thanks.

Yes, as denominator 125=5^3 or 8=2^3, numerator can be any integer.
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terminal decimal? [#permalink]  12 Sep 2010, 07:17
Which of the following fractions has a decimal equivalent that is a terminating decimal?
A. 10 /189
B. 15/196
C. 16 /225
D. 25 /144
E. 39 /128
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Re: Which of the following fractions [#permalink]  12 Sep 2010, 10:41
Nice formula for checking for 2 and 5 factors for denominator. I was dividing all numbers....
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Re: Which of the following fractions [#permalink]  13 Sep 2010, 03:20
Terminating... means has to have 2s or 5s excusively in the denominator
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Re: Which of the following fractions [#permalink]  13 Sep 2010, 21:22
great explanation on terminating decimals!
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Re: Which of the following fractions [#permalink]  14 Sep 2010, 01:43
Hi Bunuel
As per your explanation if the denominator is not in the form of 2^n 5^m then the fraction will be terminal decimal. If you look at the denominator of other answer choices they are also not in the above form
1. 189 = 3^3 *7^1
2. 196 = 2^2 * 7^2
3. 225 = 3^2 * 5^2
4. 144 = 2^4 * 3^2

So how the last answer choice is correct still not clear based on your explanation?
Re: Which of the following fractions   [#permalink] 14 Sep 2010, 01:43
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