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05 Mar 2019, 04:31
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:38) correct
38%
(01:31)
wrong
based on 378
sessions
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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. 49/224
B. 22/189
C. 37/196
D. 25/513
E. 17/175
05 Mar 2019, 04:43
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Bunuel
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
Archit3110
Major Poster
05 Mar 2019, 11:13
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Bunuel
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
