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What this base-conversion interview question tests

This is a foundational computer architecture question that asks you to convert between positional number systems—specifically from decimal (base-10) to base-7. It is a staple of technical screening because it probes whether you understand how positional notation works at a concrete level, not just in theory.

The question requires you to handle both the integer and fractional parts of a number separately, using different algorithmic approaches for each. For the integer part, you repeatedly divide and collect remainders; for the fractional part, you repeatedly multiply and extract the integer component. Precision and care with the fractional conversion are essential, since the problem asks for an exact answer to three digits.

• Positional number systems and place value
• Integer-part conversion (repeated division)
• Fractional-part conversion (repeated multiplication)
• Rounding and precision in base conversions