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Which of the following fractions has a decimal equivalent that termina

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Which of the following fractions has a decimal equivalent that termina  [#permalink]

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New post 05 Mar 2019, 04:31
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

53% (01:47) correct 47% (01:13) wrong based on 17 sessions

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Which of the following fractions has a decimal equivalent that termina  [#permalink]

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New post 05 Mar 2019, 04:43
Bunuel wrote:
Which of the following fractions has a decimal equivalent that terminates?

A. 49/224

B. 22/189

C. 37/196

D. 25/513

E. 17/175


CONCEPT: A fraction always results in a terminating decimals if the prime factors of the denominator are none other than 2 and 5

In case the denominator (in least form of fraction) has any prime factor other than 2 and 5 then the fraction results in a NON terminating decimal

A. \(49/224 = 49/(56*4) = 49/(2^5*7) = 7/2^5\) Since denominator has no prime factor other than prime factors 2 and 5 (in least form) hence it's a terminating decimal

B. \(22/189 = 22/9*21 = 22/(3^3*7)\) Since denominator has prime factor 3 and 7 which are other than prime factors 2 and 5 (in least form) hence it's NOT a terminating decimal

C. \(37/196 = 37/14^2\) Since denominator has prime factor 7 which is other than prime factors 2 and 5 (in least form) hence it's NOT a terminating decimal

D. 25/513 Since denominator has prime factor 3 which is other than prime factors 2 and 5 (in least form) hence it's NOT a terminating decimal

E. 17/175 Since denominator has prime factor 7 which is other than prime factors 2 and 5 (in least form) hence it's NOT a terminating decimal

Answer: Option A
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Re: Which of the following fractions has a decimal equivalent that termina  [#permalink]

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New post 05 Mar 2019, 11:13
Bunuel wrote:
Which of the following fractions has a decimal equivalent that terminates?

A. 49/224

B. 22/189

C. 37/196

D. 25/513

E. 17/175


a ratio of x/y will be terminating when its least form the dr has no prime factors other than 2 or 5

in this case only option A
49/224 = 7/32 = 7/2^5 ; sufficies the condition
IMO A
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Re: Which of the following fractions has a decimal equivalent that termina   [#permalink] 05 Mar 2019, 11:13
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