which of the following number represents a non terminating repeating decimal?A) 39/24 B) 3/16 c) 3/11 D) 137/ 25
Answers
Answer:
c) 3/11
Step-by-step explanation:
Because except option c all other number have denominators even or multiple of 5 which makes them terminating in nature but 11 being a prime only has terminating decimals provided the numerator is divisible by 11 and as 3 is not so hence option c is correct.
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Terminating decimals: Terminating decimals are those numbers which come to an end after few repetitions after decimal point.
Non - Terminating decimals :- A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Example :- π .
Trick :- if Prime Factors of Denominator of a Fraction is 2 or 5 or Both , it is a Terminating decimals .
if Prime Factors of Denominator of a Fraction are other than 2 or 5 , it is a Non - Terminating Repeating decimals .
Solution :-
A) 39/24
Prime Factors of Denominator :-
→ 24 = 2 * 2 * 2 * 3 = 2³ * 3
= Other Than 2 .
= Hence, Non - Terminating Repeating decimal.
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B) 3/16
Prime Factors of Denominator :-
→ 16 = 2 * 2 * 2 * 2 = 2⁴
= Only 2 .
= Hence, Terminating decimal.
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C) 3/11
Prime Factors of Denominator :-
→ 11 = 1 * 11
= Other Than 2 .
= Hence, Non - Terminating Repeating decimal.
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D) 137/25
Prime Factors of Denominator :-
→ 25 = 5 * 5 = 5²
= Only 5 .
= Hence, Terminating decimal.