---
title: "Convert (39.75)₁₀ to octal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-39-75-octal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-39-75-octal
site: BCT Engineering
---

# Convert (39.75)₁₀ to octal

Digital Logic · Chapter 1: Introduction

- Asked in: 2076 Chaitra, 1.5 marks
- Video: [Decimal To Binary, Octal, & Hexadecimal Number System conversion in Hindi | CSE GYAN](https://www.youtube.com/watch?v=-gyDAMNyu_Y) — CS Engineering Gyan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-39-75-octal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (39.75)₁₀ = (?)₈.

## Short answer

Repeatedly divide integer 39 by 8 to get 47₈, and multiply fraction 0.75 by 8 to get 0.6₈. Result is 47.6₈.

## Answer

Convert the integer part by repeated division by 8 and the fraction part by repeated multiplication by 8.

**Integer part (39):**

| Division | Quotient | Remainder |
|---|---|---|
| 39 ÷ 8 | 4 | 7 |
| 4 ÷ 8 | 0 | 4 |

Reading remainders bottom to top: $39_{10} = 47_8$.

**Fraction part (0.75):**

| Multiplication | Result | Integer digit |
|---|---|---|
| 0.75 × 8 | 6.00 | 6 |

Fraction becomes 0, so $0.75_{10} = 0.6_8$.

Check: $4 \times 8 + 7 + 6/8 = 39.75$.

**Answer:** $(39.75)_{10} = (47.6)_8$

## Check yourself

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

1. How is 39 converted to octal?
   A. Repeated division by 8, remainders read bottom to top
   B. Repeated division by 2
   C. Multiplication by 8
   D. Division by 16
   Answer: A. Divide by the target base and read remainders upward. (Key point: Integer method)

2. What is (39)10 in octal?
   A. 74
   B. 57
   C. 46
   D. 47
   Answer: D. 39 = 4x8 + 7. (Key point: Integer result)

3. What is (0.75)10 in octal?
   A. 0.75
   B. 0.06
   C. 0.7
   D. 0.6
   Answer: D. 0.75 x 8 = 6.00, giving digit 6 and ending. (Key point: Fraction)

4. What is (39.75)10 in octal?
   A. 47.75
   B. 74.6
   C. 47.6
   D. 46.6
   Answer: C. Integer 47 and fraction 0.6. (Key point: Final answer)

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