Question

What is the type of decimal expansion of the following ? (i) 164/12 (ii) 83/7 (iii) 100/15​

Answer 1

Answer:

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Answer 2

Given :- What is the type of decimal expansion of the following ? (i) 164/12 (ii) 83/7 (iii) 100/15

Solution :-

Concept used :- we have to check prime factors of denominators of given fraction .

• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

so,

(i) 164/12

→ 41/3

now, prime factors of denominator are ,

→ 3 = 1 * 3

since prime factors of denominator are other than 2 and 5 , the given fraction is a non - terminating decimal expansion .

(ii) 83/7

prime factors of denominator are ,

→ 7 = 1 * 7

since prime factors of denominator are other than 2 and 5 , the given fraction is a non - terminating decimal expansion .

(iii) 100/15

→ 100/15

→ 20/3

prime factors of denominator are ,

→ 3 = 1 * 3

since prime factors of denominator are other than 2 and 5 , the given fraction is a non - terminating decimal expansion .

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