Question

*Out of the following numbers which number has non-terminating reccuring decimal form ?* 1️⃣ 13/5 2️⃣ 23/25 3️⃣ 17/6 4️⃣ 19/8​

Answer 1

Answer:

ans: 3)17/6

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Answer 2

Solution :-

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, checking given options we get,

1) 13/5

→ Denominator = 5 = 1 * 5

since the prime factors of denominator is 5 only, the given fraction is a terminating decimal expansion .

2) 23/25

→ Denominator = 25 = 5 * 5

since the prime factors of denominator is 5 only, the given fraction is a terminating decimal expansion .

3) 17/6

→ Denominator = 6 = 2 * 3

since the prime factors of denominator is other than 2 or 5 which is 3 , the given fraction is a non - terminating decimal expansion .

4) 19/8

→ Denominator = 8 = 2 * 2 * 2

since the prime factors of denominator is 2 only, the given fraction is a terminating decimal expansion .

Hence, we can conclude that , Option (C) 17/6 is the number which has non-terminating reccuring decimal form .

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