Decimal Expansion of Real Numbers MCQs

Q1. The decimal expansion of 7/16 terminates after how many decimal places?

• A.4
• B.3
• C.5
• D.7

Answer: A. 4

Reading off the stem: 7; 16. What we must find: how many decimal places?. Governing law - max(4, 0) = 4. This is the equation that links the given quantities to the unknown (math, chapter 'Number Systems'). Numerically: 16 = 2^4 × → max(4, 0) = 4. Why this is the right approach - terminates after 4 decimal places. Hence the answer is A) 4. The other choices: option B) '3' doesn't hold - Power of 2 or 5 in denominator: take the max; option C) '5' misses the point - 16 = 2^4 × 5^0; max = 4; option D) '7' is wrong because Count the decimal places, not the numerator.

Q2. The decimal expansion of 9/25 terminates after how many decimal places?

• A.2
• B.1
• C.3
• D.9

Answer: A. 2

Reading off the stem: 9; 25. To find: how many decimal places?. Key equation - max(0, 2) = 2. This is the equation that links the given quantities to the unknown (math, chapter 'Number Systems'). Plugging the values in: 25 = 2^0 × → max(0, 2) = 2. Why this is the right approach - terminates after 2 decimal places. Therefore the answer is A) 2. Wrong options at a glance: option B) '1' fails since Power of 2 or 5 in denominator: take the max; option C) '3' is wrong because 25 = 2^0 × 5^2; max = 2; option D) '9' fails since Count the decimal places, not the numerator.

Q3. A fraction p/q in lowest terms has p + q = 17 and a decimal that terminates in exactly 2 places. Find p - q.

• A.9
• B.17
• C.-9
• D.10

Answer: A. 9

Quick parse - a typical math numerical. The data on the table: 17, 2. We are after Find p - q. Tool of choice - q must be 2^a5^b giving exactly 2 places and p+q=17 with gcd(p,q)=1. Rearrange it for the unknown before substituting. Numbers in: q must be 2^a5^b giving exactly 2 places and p+q=17 with gcd(p,q)=1 → p-q = 13-4 = 9. Lock in option A) 9. Trap-watch: option B) '17' fails since p+q is given; the question asks p-q; option C) '-9' fails since Order: p - q.