Floating Point — Test 1

Correct Answer: D. False
Explanation: 0.1 and 0.2 have no exact binary representation. Their sum is 0.30000000000000004. Use math.isclose to compare floats. ALSO KNOW (related points): • Which of these decimal values can be represented exactly in binary floating point? → 0.375 • In C++ or Java, what does the expression NaN == NaN evaluate to? → false • In C++, given float f = 0.1f; double d = 0.1;, what does f == d evaluate to? → false • What does float('inf') > 10**1000 evaluate to in Python? → True

Correct Answer: D. 0.375
Explanation: 0.375 = 0.011 in binary (1/4 + 1/8). The others repeat infinitely in binary.

Correct Answer: B. 1 sign bit, 11 exponent bits, 52 fraction bits
Explanation: Single precision (32-bit) uses 1/8/23. Double precision uses 1/11/52. ALSO KNOW (related points): • Approximately how many significant decimal digits do float and double provide? → float about 7; double about 15–16

Correct Answer: B. float about 7; double about 15–16
Explanation: 24 bits of precision is about 7.2 decimal digits; 53 bits is about 15.9.

Correct Answer: C. false
Explanation: Under IEEE 754, NaN compares unequal to everything, including itself. x != x is a common test for NaN.

Correct Answer: A. ZeroDivisionError
Explanation: Python raises an exception even for float division by zero. In C++ and Java, IEEE arithmetic gives +Infinity. ALSO KNOW (related points): • In Java, what does 1.0 / 0 evaluate to? → Infinity • What is type(1e20) in Python? → float

Correct Answer: D. Infinity
Explanation: Floating-point division by zero gives Infinity. Only integer division by zero throws ArithmeticException.

Correct Answer: C. 2 and 0
Explanation: Python 3 uses round-half-to-even (banker's rounding), so ties go to the nearest even number. ALSO KNOW (related points): • What is -7.0 // 2 in Python? → -4.0

Correct Answer: B. false
Explanation: f holds a less precise approximation of 0.1. When it is promoted to double, it differs from d.

Correct Answer: C. True
Explanation: Infinity compares greater than any finite number, including very large Python ints.