How is 37 converted to octal?

Repeated division by 8, giving 45

How is 0.85 converted to octal?

Repeated multiplication by 8, taking integer parts

2082 Shrawan · 1 mark

Convert (37.85)₁₀ to octal

Short answer

Integer part: 37÷8=4 r5, 4÷8=0 r4 → 45₈. Fractional part: 0.85×8=6.8(6), 0.8×8=6.4(6), 0.4×8=3.2(3), 0.2×8=1.6(1), 0.6×8=4.8(4) then repeats. So (37.85)₁₀ ≈ (45.66314)₈.

Convert (37.85)₁₀ = (?)₈.

Integer part: 37 ÷ 8 = 4 r 5; 4 ÷ 8 = 0 r 4 → $(45)_8$ .

Fraction part (multiply by 8):

Step	Result	Digit
0.85 × 8	6.8	6
0.8 × 8	6.4	6
0.4 × 8	3.2	3
0.2 × 8	1.6	1
0.6 × 8	4.8	4

The digits then repeat (6, 3, 1, 4, …).

Answer: $(37.85)_{10} \approx (45.66314)_8$

✓ Answer checked by Claude Opus 5.5 (high effort)

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