Decimal to octal conversion Convert the decimal number 281 to base-8 (octal).

Introduction / Context:
Converting from decimal to octal is done by repeated division by 8 and collecting remainders. Reading the remainders backward gives the octal digits.

Given Data / Assumptions:

• Number: 281 (base 10).
• Target base: 8.

Concept / Approach:
Use integer division by 8. Each remainder is a base-8 digit from 0 to 7. Stop when the quotient reaches 0, then write remainders from last to first.

Step-by-Step Solution:

Verification / Alternative check:
Convert back: 48^2 + 38 + 1 = 256 + 24 + 1 = 281, confirming correctness.

Why Other Options Are Wrong:

• 134₈ / 331₈ / 133₈: These evaluate to 92, 217, and 91 respectively, not 281.

Common Pitfalls:
Writing the remainders in forward order instead of reverse, or using base-10 powers instead of base-8.

Final Answer:
431₈