Number Systems 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 surfer rides a wave measured at 0.6 metres of face; rational or irrational?

• A.Irrational
• B.Neither rational nor irrational
• C.Undeterminable
• D.Rational

Answer: D. Rational

0.6: 0.6 is a terminating decimal equal to a fraction. Hence the number is rational.