Question

*Fill in the blank: The decimal expansion of 2/11 is ________.*

1️⃣ Terminating
2️⃣ Non terminating
3️⃣ Non terminating and repeating
4️⃣ Non terminating and non repeating​

Answer 1

Given :- Fill in the blank: The decimal expansion of 2/11 is ________.*

1️⃣ Terminating

2️⃣ Non terminating

3️⃣ Non terminating and repeating

4️⃣ Non terminating and non repeating

Answer :- 3️⃣ Non terminating and repeating .

Explanation :-

• 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,

→ 2/11 = denominator = 11

→ prime factors of 11 = 1 * 11 ≠ 2 or 5 .

therefore, 2/11 is Non terminating and repeating decimal .

[Note :- Non terminating and non repeating decimal are that continues endlessly, with no group of digits repeating .]

Learn more :-

let a and b positive integers such that 90 less than a+b less than 99 and 0.9 less than a/b less than 0.91. Find ab/46

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Answer 2

Answer:

Non terminating and repeating