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Intern  Joined: 06 May 2009
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Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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Question Stats: 61% (01:12) correct 39% (01:10) wrong based on 620 sessions

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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

Originally posted by ankur55 on 09 Jul 2009, 09:29.
Last edited by Bunuel on 01 Feb 2019, 00:01, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 64967
Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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38
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

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 $$2*5^2$$. 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:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

Questions testing this concept:
http://gmatclub.com/forum/does-the-deci ... 89566.html
http://gmatclub.com/forum/any-decimal-t ... 01964.html
http://gmatclub.com/forum/if-a-b-c-d-an ... 25789.html
http://gmatclub.com/forum/700-question-94641.html
http://gmatclub.com/forum/is-r-s2-is-a- ... 91360.html
http://gmatclub.com/forum/pl-explain-89566.html
http://gmatclub.com/forum/which-of-the- ... 88937.html
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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35
19

For a fraction to be a terminating decimal the denominator can contain only the prime factors 2 and/or 5 i.e. the denominator should be in the form $$2^a5^b$$

Looking at each denominator.

A. 189 has the prime factor 3 so the fraction is not a terminating decimal.
B. 196 has the prime factor 7 so the fraction is not a terminating decimal.
C. 225 has the prime factor 3 so the fraction is not a terminating decimal.
D. 144 has the prime factor 3 so the fraction is not a terminating decimal.
E. 128 has the prime factor 2 only and can be written in the form $$2^75^0$$ which makes the fraction a terminating decimal.
##### General Discussion
Intern  Joined: 15 Apr 2008
Posts: 44
Location: Moscow
Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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14
1
One important point: you should look at numerator as well, as it can simplify denominator. For example, $$18/225$$ is a terminating decimal: $$18/225=\frac{3*3*2}{3*3*5*5}=\frac{2}{5*5}$$.
However, this problem doesn't try to trick you this way.
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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3
2
akankshasoneja wrote:
salsal 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

is there any simple method to find it?

Denominators of options a,c,d contains powers of 3...numerators of these options when divided by 3 will have non-terminating decimals
Denominator of option b contains power of 7...numerator 15 when divided by 7 will give non terminating decimal
Option E has denominator in powers of 2...so when 39 divided by 2 will give a terminating decimal

Hope it helps
Math Expert V
Joined: 02 Sep 2009
Posts: 64967
Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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11
23
To practice more check Terminating and Recurring Decimals Problems in our Special Questions Directory.

Hope it helps.
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Director  Joined: 29 Nov 2012
Posts: 673
Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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1
You can solve this question in less than 30 seconds if you understand the concept of terminating decimal. The denominator must have only power's of 2 or 5 in the denominator no other powers ( if it has any other prime factors like 3,7, etc it won't be terminating). 2's and 5's can be in any possible combination but it must only have 2's and 5's

a) 10/189

denominator sum of digits is 18 so its divisible by 3 eliminate

b) 15/196

This has a prime factor of 7 when do the prime factorization of the denominator.. Eliminate

c) 16/225

denominator sum of digits is 9 so its divisible by 3 eliminate

d) 25/144

denominator sum of digits is 9 so its divisible by 3 eliminate

Math Expert V
Joined: 02 Sep 2009
Posts: 64967
Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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fozzzy wrote:
You can solve this question in less than 30 seconds if you understand the concept of terminating decimal. The denominator must have only power's of 2 or 5 in the denominator no other powers ( if it has any other prime factors like 3,7, etc it won't be terminating). 2's and 5's can be in any possible combination but it must only have 2's and 5's

This is true if a fraction is reduced to its lowest term.

Consider this: the denominator of 3/30 has other primes than 2 or 5, but 3/30 IS a terminating decimal because 3 in the denominator gets reduced: 3/30=1/10=0.1.

Hope it's clear.
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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1
Bunuel wrote:
salsal 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

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 $$2*5^2$$. 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:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128
Math Expert V
Joined: 02 Sep 2009
Posts: 64967
Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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2
AccipiterQ wrote:
Bunuel wrote:
salsal 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

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 $$2*5^2$$. 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:

Only option E (when reduced to its lowest form) has the denominator of the form $$2^n5^m$$: 39/128=39/2^7.

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.

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128

Yes, it is 128 = 2^7*5^0.
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GMAT 1: 670 Q39 V41
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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Bunuel wrote:
AccipiterQ wrote:

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128

Yes, it is 128 = 2^7*5^0.

So ANY number with a 2^x or 5^x (where x is greater than or equal to 1) will fall into this then?

I'm confused though, so 6/15 a terminating decimal, because 15 is 5^1*3^1*2^0, but then why is 16/225 is not terminating? It follows the same pattern; 225 is 5^2*3^2*2^0
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Posts: 64967
Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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AccipiterQ wrote:
Bunuel wrote:
AccipiterQ wrote:

I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128

Yes, it is 128 = 2^7*5^0.

So ANY number with a 2^x or 5^x (where x is greater than or equal to 1) will fall into this then?

I'm confused though, so 6/15 a terminating decimal, because 15 is 5^1*3^1*2^0, but then why is 16/225 is not terminating? It follows the same pattern; 225 is 5^2*3^2*2^0

6/15=6/(3*5) is a terminating decimal because extra 3 in the denominator is reduced and we get 2/5 (the denominator is in the form of 2^n*5^m).

16/225=16/(3^2*5^2) is not a terminating decimal because extra 3^2 in the denominator is not reduced to get the denominator in the form of 2^n*5^m.

Hope it's clear.
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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Top Contributor
salsal 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

NOTE: this is one of those questions that require us to check/test each answer choice.
In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... -questions

Cheers,
Brent
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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If numerator and denominator in fraction doesn’t have any common factor and the denominator has a prime factor except 2 and 5, then it is going to be non terminating decimal.
Out of every option only Option E has 2 as the prime factor. Rest all have 3also. Hence option E s the answer
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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salsal 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

Check out this post for a detailed discussion on terminating decimals:
https://www.veritasprep.com/blog/2013/1 ... -the-gmat/
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Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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salsal 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

A decimal will terminate when the equivalent fraction in lowest terms has a denominator that breaks down to primes of 2’s only, 5’s only, or both 2’s and 5’s only.

Looking at our answer choices we see that 39/128 is a terminating decimal since 128 = 2^7.

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GMAT 1: 600 Q46 V27 Re: Which of the following fractions has a decimal equivalent that is a te  [#permalink]

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ankur55 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

Okay. So I know for a decimal to be terminating decimal it should have factors 2 and 5 in the denominator.

But GMAC provided no such option (at least directly).

But Clearly A B C D have perfect squares in denominator. So clearly the answer is E. (without wasting any time and with confidence) Brilliant Question again!
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You are missing on great learning if you don't know what this is: Project SC Butler Re: Which of the following fractions has a decimal equivalent that is a te   [#permalink] 10 Dec 2019, 14:43

# Which of the following fractions has a decimal equivalent that is a te  