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Which of the following has a decimal equivalent that is a terminating

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Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 31 Dec 2018, 01:25
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Which of the following has a decimal equivalent that is a terminating decimal?

I. 1/128
II. 1/225
III. 1/384

A. I only
B. II only
C. I and II
D. I and III
E. I, II and III

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Re: Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 31 Dec 2018, 01:37
1
For a fraction to have a decimal equivalent that is a terminating decimal, the denominator of the fraction must be power(s) of 2, or of 5, or of both 2 & 5.

I. 1/128
1/128 = 1/(2^7). Hence, this fraction will have a decimal equivalent that is a terminating decimal

II. 1/225
1/225 = 1/(5^2 x 3^2). Hence, this fraction will have a decimal equivalent that is NOT a terminating decimal.

III. 1/384
1/384 = 1/(2^7 x 3). Hence, this fraction will have a decimal equivalent that is NOT a terminating decimal.

Therefore, the Correct Answer is Option A. I only
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Re: Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 31 Dec 2018, 10:08
DisciplinedPrep wrote:
For a fraction to have a decimal equivalent that is a terminating decimal, the denominator of the fraction must be power(s) of 2, or of 5, or of both 2 & 5.

I. 1/128
1/128 = 1/(2^7). Hence, this fraction will have a decimal equivalent that is a terminating decimal

II. 1/225
1/225 = 1/(5^2 x 3^2). Hence, this fraction will have a decimal equivalent that is NOT a terminating decimal.

III. 1/384
1/384 = 1/(2^7 x 3). Hence, this fraction will have a decimal equivalent that is NOT a terminating decimal.

Therefore, the Correct Answer is Option A. I only


Hello!

Thanks for the explanation, I just have one question related to the wording:

"For a fraction to have a decimal equivalent that is a terminating decimal, the denominator of the fraction must be power(s) of 2, or of 5, or of both 2 & 5."

Is it JUST powers of 2 and 5? Because all the factions above have powers of either 2 or 5.

Thank you!
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Re: Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 31 Dec 2018, 21:42
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jfranciscocuencag wrote:
DisciplinedPrep wrote:
For a fraction to have a decimal equivalent that is a terminating decimal, the denominator of the fraction must be power(s) of 2, or of 5, or of both 2 & 5.

I. 1/128
1/128 = 1/(2^7). Hence, this fraction will have a decimal equivalent that is a terminating decimal

II. 1/225
1/225 = 1/(5^2 x 3^2). Hence, this fraction will have a decimal equivalent that is NOT a terminating decimal.

III. 1/384
1/384 = 1/(2^7 x 3). Hence, this fraction will have a decimal equivalent that is NOT a terminating decimal.

Therefore, the Correct Answer is Option A. I only


Hello!

Thanks for the explanation, I just have one question related to the wording:

"For a fraction to have a decimal equivalent that is a terminating decimal, the denominator of the fraction must be power(s) of 2, or of 5, or of both 2 & 5."

Is it JUST powers of 2 and 5? Because all the factions above have powers of either 2 or 5.

Thank you!


Hi,
A fraction can be terminating if it has powers of 2 or 5 or both in the denominator.
For eg. 1/2 = 0.5; 1/5 = 0.2; 1/10 = 0.1.
See the wording in the question can be understood easily by above examples.

On the other hand when the denominator is other than 2 or 5 or 2&5 then the fraction is not terminating
for eg. 1/3 =0.3333333....
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Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 02 Jan 2019, 04:25

Solution


To find:
    • Which of the given options has a decimal equivalent that is terminating decimal?

Approach and Working:
We know that if denominator contains either 2 or 4 or 5 or 8 or combination of these then the fraction will be a terminating decimal
    I. \(128 = 2^7\) – Thus, \(\frac{1}{128}\) is a terminating decimal
    II. \(225 = 3^2 * 5^2\) – Thus, \(\frac{1}{225}\) is not a terminating decimal
    III. \(384 = 2^7 * 3\) – Thus, \(\frac{1}{384}\) is not a terminating decimal

Hence, the correct answer is Option A

Answer: A

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Re: Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 02 Jan 2019, 04:31
UB001 wrote:
Which of the following has a decimal equivalent that is a terminating decimal?

I. 1/128
II. 1/225
III. 1/384

A. I only
B. II only
C. I and II
D. I and III
E. I, II and III



Since the numerator of all the 3 numbers are 1. We can check only for denominators.

128 - 2^7 ---> Only 2's. Hence Terminating Decimal
225 - 3*3*5*5 --> Non-Terminating Decimal
384 - 2^7 * 3 ---> Non-Terminating Decimal
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Re: Which of the following has a decimal equivalent that is a terminating  [#permalink]

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New post 12 Jan 2019, 01:30
UB001 wrote:
Which of the following has a decimal equivalent that is a terminating decimal?

I. 1/128
II. 1/225
III. 1/384

A. I only
B. II only
C. I and II
D. I and III
E. I, II and III



Terminating decimal means the denominator is of the form \(2^a*5^b\), where a and b can be any NON-NEGATIVE integer

let us therefore, concentrate only on denominators..
I. 1/128.... denominator is 128 => \(128=2^7\)...YES
II. 1/225.... denominator is 225 => \(225=5^2*7\)...NO
III. 1/384.... denominator is 384 => 384 is a multiple of 3 as 3+8+4=12 and 12 is a multiple of 3...NO

Only I,

A
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Re: Which of the following has a decimal equivalent that is a terminating   [#permalink] 12 Jan 2019, 01:30
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