---
title: "Convert (37.85)₁₀ to octal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-37-85-octal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-37-85-octal
site: BCT Engineering
---

# Convert (37.85)₁₀ to octal

Digital Logic · Chapter 1: Introduction

- Asked in: 2082 Shrawan, 1 marks
- Video: [Decimal to Octal Conversion](https://www.youtube.com/watch?v=ayul1fmZd0Y) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-37-85-octal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (37.85)₁₀ = (?)₈.

## 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.

## Answer

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

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is 37 converted to octal?
   A. Repeated division by 8, giving 45
   B. Repeated division by 2
   C. Repeated multiplication by 8
   D. Division by 10
   Answer: A. 37 / 8 = 4 r 5; 4 / 8 = 0 r 4. (Key point: Integer method)

2. How is 0.85 converted to octal?
   A. Repeated division by 8
   B. Repeated multiplication by 8, taking integer parts
   C. Multiplication by 2
   D. Multiplication by 16
   Answer: B. 0.85 x 8 = 6.8 gives digit 6. (Key point: Fraction method)

3. What is (37.85) decimal in octal?
   A. 54.66314
   B. 45.85
   C. 45.66314 (approx)
   D. 25.66314
   Answer: C. Integer 45 and fraction digits 6,6,3,1,4. (Key point: Final answer)

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