Fractional conversion 243.1 base 5 – UGC NET Question

The number 243.1₅ is interpreted using powers of 5, including negative powers for the fractional part. Its expansion is 2×5² + 4×5¹ + 3×5⁰ + 1×5⁻¹, which equals 2×25 + 4×5 + 3×1 + 1/5. This gives 50 + 20 + 3 + 0.2 = 73.2 in decimal. Thus, the correct decimal value of 243.1₅ is 73.2, making option A correct.

Option A:
Option A matches the exact sum from the base-5 positional expansion, including the fractional 0.2 term from 5⁻¹.

Option B:
Option B underestimates the value; the integer part alone is 73, so 72.2 cannot be correct.

Option C:
Option C has the right integer part but the wrong fractional part; 1×5⁻¹ = 0.2, not 0.4.

Option D:
Option D overestimates the integer part; it would require larger digits or different place values than in 243.1₅.