Octal-to-decimal conversion — clarify base explicitly Convert 1731 (base 8) to its decimal (base 10) value.

Introduction / Context:
Numbers may be written in different bases. Octal (base 8) is common in low-level computing contexts. This problem converts the octal number 1731_8 to decimal, reinforcing positional notation and powers for non-decimal bases.

Given Data / Assumptions:

• Given octal number: 1731 in base 8.
• Digits are valid octal digits (0–7 only).
• We must compute an exact integer decimal value.

Concept / Approach:

For base b, a number d_n d_{n-1} … d_1 d_0 equals Σ(d_i * b^i). For octal, b = 8. Expand each digit by its positional weight, then sum. No fractional part is present here.

Step-by-Step Solution:

Verification / Alternative check:

Convert back to octal using repeated division by 8 on 985 or confirm via a calculator that 985 / 8 = 123 remainder 1, continuing to remainders 3, 7, 1 upward to reconstruct 1731.

Why Other Options Are Wrong:

216.4: suggests a fractional decimal result (not applicable; all digits are integral and valid octal, so the result is an integer).

3D9: uses hexadecimal notation mixed with decimal; it is neither a pure decimal numeral nor the correct hex of this value in the option context.

1123: corresponds to a different expansion (for example, misplacing weights), not the correct sum of 512 + 448 + 24 + 1.

Common Pitfalls:

Reading the number as base 10, confusing base subscripts, or mistakenly squaring 8 instead of using the correct powers per position. Always label the base explicitly to avoid ambiguity.

Final Answer:

985