Decimal expansions: terminating and recurring MCQs

Q1. After how many decimal places does 3/8 terminate?

• A.9
• B.4
• C.3
• D.5

Answer: C. 3

Given 3, 8, asked for how many decimal places does 3/8 terminate?. By a rational p/q in lowest terms terminates iff q = 2^m x 5^n, otherwise it is non-terminating recurring. a rational p/q in lowest terms terminates iff q = 2^m x 5^n, otherwise it is non-terminating recurring → hence the required value = 3. reduce the given fraction and inspect the denominator's prime factorisation. Hence option C) 3. Others fail: option A) '9' is incorrect: Wrong: a common multi-step slip gives this; option B) '4' fails since Wrong: a step was skipped or HCF/LCM swapped.

Q2. The decimal expansion of 3/16 terminates after how many places?

• A.6
• B.5
• C.4
• D.7

Answer: C. 4

Q3. How many digits are there after the decimal point in the (terminating) expansion of 3/25?

• A.13
• B.3
• C.2
• D.4

Answer: C. 2