Math worksheet featuring multiple-choice questions on decimal and octal number conversions.

Let's solve each question from the Decimal and Octal - MCQ worksheet step by step. The questions involve converting between decimal (base-10) and octal (base-8) number systems.

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Question 1: The octal equivalent of 32₁₀ is

We need to convert decimal 32 to octal.

Step-by-step conversion:

Divide 32 by 8:
- 32 ÷ 8 = 4 remainder 0
- 4 ÷ 8 = 0 remainder 4

Now read the remainders from bottom to top: 40₈

✔ Answer: b) 40₈

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Question 2: Which of the following is the octal equivalent of 428₁₀?

Convert 428 to octal.

Divide by 8 repeatedly:

- 428 ÷ 8 = 53 remainder 4
- 53 ÷ 8 = 6 remainder 5
- 6 ÷ 8 = 0 remainder 6

Read remainders from bottom to top: 654₈

✔ Answer: b) 654₈

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Question 3: The decimal equivalent of 65₈ is

Convert 65₈ (octal) to decimal.

Use place values (powers of 8):

- 6 × 8¹ = 6 × 8 = 48
- 5 × 8⁰ = 5 × 1 = 5

Add: 48 + 5 = 53₁₀

✔ Answer: c) 53₁₀

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Question 4: Which of the following is the decimal equivalent of 1574₈?

Convert 1574₈ to decimal.

Break it down:

- 1 × 8³ = 1 × 512 = 512
- 5 × 8² = 5 × 64 = 320
- 7 × 8¹ = 7 × 8 = 56
- 4 × 8⁰ = 4 × 1 = 4

Add: 512 + 320 = 832; 832 + 56 = 888; 888 + 4 = 892₁₀

✔ Answer: a) 892₁₀

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Question 5: The octal equivalent of 753₁₀ is

Convert 753 to octal.

Divide by 8:

- 753 ÷ 8 = 94 remainder 1
- 94 ÷ 8 = 11 remainder 6
- 11 ÷ 8 = 1 remainder 3
- 1 ÷ 8 = 0 remainder 1

Remainders from bottom to top: 1361₈

✔ Answer: d) 1361₈

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Question 6: Which of the following is the decimal equivalent of 5627₈?

Convert 5627₈ to decimal.

Break down:

- 5 × 8³ = 5 × 512 = 2560
- 6 × 8² = 6 × 64 = 384
- 2 × 8¹ = 2 × 8 = 16
- 7 × 8⁰ = 7 × 1 = 7

Add: 2560 + 384 = 2944; 2944 + 16 = 2960; 2960 + 7 = 2967₁₀

✔ Answer: a) 2967₁₀

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Question 7: The octal equivalent of 2081₁₀ is

Convert 2081 to octal.

Divide by 8:

- 2081 ÷ 8 = 260 remainder 1
- 260 ÷ 8 = 32 remainder 4
- 32 ÷ 8 = 4 remainder 0
- 4 ÷ 8 = 0 remainder 4

Remainders from bottom to top: 4041₈

✔ Answer: d) 4041₈

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1 | b) 40₈ |
| 2 | b) 654₈ |
| 3 | c) 53₁₀ |
| 4 | a) 892₁₀ |
| 5 | d) 1361₈ |
| 6 | a) 2967₁₀ |
| 7 | d) 4041₈ |

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