Convert the decimal number 99 (base 10) to its octal (base 8) representation.

Introduction / Context:
Octal (base 8) was historically used in computing because each octal digit maps neatly to three binary bits. Converting between decimal and octal is still useful for understanding legacy systems, permissions in Unix (e.g., 755), and compact binary representations. Here we convert 99₁₀ to base 8.

Given Data / Assumptions:

• Value: 99 decimal.
• Target base: octal (digits 0–7).
• Use repeated division by 8 or binary grouping as methods.

Concept / Approach:
With repeated division by 8, we divide the decimal number by 8, record the remainder (octal digit), and continue with the quotient until it becomes 0. Reading remainders from last to first gives the octal number. Alternatively, convert 99 to binary (1100011₂) and group in 3-bit chunks to get octal 143 directly.

Step-by-Step Solution:
99 / 8 = 12 remainder 3 → least significant octal digit = 3.12 / 8 = 1 remainder 4 → next octal digit = 4.1 / 8 = 0 remainder 1 → most significant octal digit = 1.Reading MSB to LSB: 1 4 3 → 143 (base 8).

Verification / Alternative check:
Binary grouping: 99₁₀ = 1100011₂ → 001 100 011 → 1 4 3 in octal. Also, compute back: 164 + 48 + 3 = 64 + 32 + 3 = 99, confirming correctness.

Why Other Options Are Wrong:
121₈ = 81 decimal; 124₈ = 84 decimal; 119 is not a valid octal number (9 is invalid); “None” is wrong because 143 is correct.

Common Pitfalls:
Forgetting to read remainders in reverse; using base 16 groupings by mistake; including invalid digits 8 or 9 in octal results.

Final Answer:
143