Change 432$_{five}$  to a number in base three.

Step 1: Analyze the question We need to convert a base five number to base three. The easiest route is to convert to base ten first, then to base three.

Step 2: Convert 432₅ to base ten 432₅ = 4×5² + 3×5¹ + 2×5⁰ = 4×25 + 3×5 + 2 = 100 + 15 + 2 = 117₁₀

Step 3: Convert 117₁₀ to base three Divide repeatedly by 3 and record the remainders:

• 117 ÷ 3 = 39 remainder 0
• 39 ÷ 3 = 13 remainder 0
• 13 ÷ 3 = 4 remainder 1
• 4 ÷ 3 = 1 remainder 1
• 1 ÷ 3 = 0 remainder 1

Read the remainders from bottom to top: 11100₃

Step 4: Check 1×81 + 1×27 + 1×9 + 0×3 + 0×1 = 81 + 27 + 9 = 117 ✓

Answer: 11100₃, which is option B.

Exam tip: For conversions between two non-decimal bases, go through base ten. Always verify by converting your answer back. It takes seconds and catches errors. Also, remember to read the remainders from the bottom up.