Decimal to Octal Conversion Worksheet
Worksheet for converting decimal and octal numbers, featuring exercises to convert between decimal and octal systems.
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Show Answer Key & Explanations
Step-by-step solution for: Number Systems Worksheets | Dynamically Created Number Systems ...
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Show Answer Key & Explanations
Step-by-step solution for: Number Systems Worksheets | Dynamically Created Number Systems ...
Let’s solve each problem step by step. We’ll convert decimal numbers to octal (base 8) and octal numbers to decimal (base 10).
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Part 1: Convert Decimal to Octal
To convert a decimal number to octal, we divide the number by 8 repeatedly and write down the remainders in reverse order.
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1) 138₁₀ → ?₈
138 ÷ 8 = 17 remainder 2
17 ÷ 8 = 2 remainder 1
2 ÷ 8 = 0 remainder 2
Read remainders from bottom to top: 212
✔ Answer: 212₈
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2) 740₁₀ → ?₈
740 ÷ 8 = 92 remainder 4
92 ÷ 8 = 11 remainder 4
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Remainders: 1, 3, 4, 4 → 1344
✔ Answer: 1344₈
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3) 248₁₀ → ?₈
248 ÷ 8 = 31 remainder 0
31 ÷ 8 = 3 remainder 7
3 ÷ 8 = 0 remainder 3
Remainders: 3, 7, 0 → 370
✔ Answer: 370₈
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4) 709₁₀ → ?₈
709 ÷ 8 = 88 remainder 5
88 ÷ 8 = 11 remainder 0
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Remainders: 1, 3, 0, 5 → 1305
✔ Answer: 1305₈
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5) 494₁₀ → ?₈
494 ÷ 8 = 61 remainder 6
61 ÷ 8 = 7 remainder 5
7 ÷ 8 = 0 remainder 7
Remainders: 7, 5, 6 → 756
✔ Answer: 756₈
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6) 601₁₀ → ?₈
601 ÷ 8 = 75 remainder 1
75 ÷ 8 = 9 remainder 3
9 ÷ 8 = 1 remainder 1
1 ÷ 8 = 0 remainder 1
Remainders: 1, 1, 3, 1 → 1131
✔ Answer: 1131₈
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7) 288₁₀ → ?₈
288 ÷ 8 = 36 remainder 0
36 ÷ 8 = 4 remainder 4
4 ÷ 8 = 0 remainder 4
Remainders: 4, 4, 0 → 440
✔ Answer: 440₈
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8) 762₁₀ → ?₈
762 ÷ 8 = 95 remainder 2
95 ÷ 8 = 11 remainder 7
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Remainders: 1, 3, 7, 2 → 1372
✔ Answer: 1372₈
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Part 2: Convert Octal to Decimal
To convert octal to decimal, multiply each digit by 8 raised to the power of its position (starting from 0 on the right), then add them up.
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9) 707₈ → ?₁₀
Digits: 7 (hundreds place? No — positions from right: 0,1,2)
So:
7 × 8² = 7 × 64 = 448
0 × 8¹ = 0 × 8 = 0
7 × 8⁰ = 7 × 1 = 7
Total: 448 + 0 + 7 = 455
✔ Answer: 455₁₀
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10) 273₈ → ?₁₀
2 × 8² = 2 × 64 = 128
7 × 8¹ = 7 × 8 = 56
3 × 8⁰ = 3 × 1 = 3
Total: 128 + 56 + 3 = 187
✔ Answer: 187₁₀
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11) 531₈ → ?₁₀
5 × 64 = 320
3 × 8 = 24
1 × 1 = 1
Total: 320 + 24 + 1 = 345
✔ Answer: 345₁₀
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12) 1177₈ → ?₁₀
This is 4 digits: positions 3,2,1,0 from left to right? Wait — better to go right to left for powers.
Actually, let’s index from right:
Rightmost digit is position 0.
So:
1 × 8³ = 1 × 512 = 512
1 × 8² = 1 × 64 = 64
7 × 8¹ = 7 × 8 = 56
7 × 8⁰ = 7 × 1 = 7
Wait — that’s if it’s written as 1 1 7 7 from left to right.
Yes:
Digit at position 3 (leftmost): 1 → 1×8³ = 512
Position 2: 1 → 1×8² = 64
Position 1: 7 → 7×8¹ = 56
Position 0: 7 → 7×8⁰ = 7
Sum: 512 + 64 = 576; 576 + 56 = 632; 632 + 7 = 639
✔ Answer: 639₁₀
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13) 415₈ → ?₁₀
4 × 64 = 256
1 × 8 = 8
5 × 1 = 5
Total: 256 + 8 + 5 = 269
✔ Answer: 269₁₀
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14) 263₈ → ?₁₀
2 × 64 = 128
6 × 8 = 48
3 × 1 = 3
Total: 128 + 48 = 176; 176 + 3 = 179
✔ Answer: 179₁₀
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15) 744₈ → ?₁₀
7 × 64 = 448
4 × 8 = 32
4 × 1 = 4
Total: 448 + 32 = 480; 480 + 4 = 484
✔ Answer: 484₁₀
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16) 377₈ → ?₁₀
3 × 64 = 192
7 × 8 = 56
7 × 1 = 7
Total: 192 + 56 = 248; 248 + 7 = 255
✔ Answer: 255₁₀
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Final Answer:
1) 212
2) 1344
3) 370
4) 1305
5) 756
6) 1131
7) 440
8) 1372
9) 455
10) 187
11) 345
12) 639
13) 269
14) 179
15) 484
16) 255
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Part 1: Convert Decimal to Octal
To convert a decimal number to octal, we divide the number by 8 repeatedly and write down the remainders in reverse order.
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1) 138₁₀ → ?₈
138 ÷ 8 = 17 remainder 2
17 ÷ 8 = 2 remainder 1
2 ÷ 8 = 0 remainder 2
Read remainders from bottom to top: 212
✔ Answer: 212₈
---
2) 740₁₀ → ?₈
740 ÷ 8 = 92 remainder 4
92 ÷ 8 = 11 remainder 4
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Remainders: 1, 3, 4, 4 → 1344
✔ Answer: 1344₈
---
3) 248₁₀ → ?₈
248 ÷ 8 = 31 remainder 0
31 ÷ 8 = 3 remainder 7
3 ÷ 8 = 0 remainder 3
Remainders: 3, 7, 0 → 370
✔ Answer: 370₈
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4) 709₁₀ → ?₈
709 ÷ 8 = 88 remainder 5
88 ÷ 8 = 11 remainder 0
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Remainders: 1, 3, 0, 5 → 1305
✔ Answer: 1305₈
---
5) 494₁₀ → ?₈
494 ÷ 8 = 61 remainder 6
61 ÷ 8 = 7 remainder 5
7 ÷ 8 = 0 remainder 7
Remainders: 7, 5, 6 → 756
✔ Answer: 756₈
---
6) 601₁₀ → ?₈
601 ÷ 8 = 75 remainder 1
75 ÷ 8 = 9 remainder 3
9 ÷ 8 = 1 remainder 1
1 ÷ 8 = 0 remainder 1
Remainders: 1, 1, 3, 1 → 1131
✔ Answer: 1131₈
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7) 288₁₀ → ?₈
288 ÷ 8 = 36 remainder 0
36 ÷ 8 = 4 remainder 4
4 ÷ 8 = 0 remainder 4
Remainders: 4, 4, 0 → 440
✔ Answer: 440₈
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8) 762₁₀ → ?₈
762 ÷ 8 = 95 remainder 2
95 ÷ 8 = 11 remainder 7
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Remainders: 1, 3, 7, 2 → 1372
✔ Answer: 1372₈
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Part 2: Convert Octal to Decimal
To convert octal to decimal, multiply each digit by 8 raised to the power of its position (starting from 0 on the right), then add them up.
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9) 707₈ → ?₁₀
Digits: 7 (hundreds place? No — positions from right: 0,1,2)
So:
7 × 8² = 7 × 64 = 448
0 × 8¹ = 0 × 8 = 0
7 × 8⁰ = 7 × 1 = 7
Total: 448 + 0 + 7 = 455
✔ Answer: 455₁₀
---
10) 273₈ → ?₁₀
2 × 8² = 2 × 64 = 128
7 × 8¹ = 7 × 8 = 56
3 × 8⁰ = 3 × 1 = 3
Total: 128 + 56 + 3 = 187
✔ Answer: 187₁₀
---
11) 531₈ → ?₁₀
5 × 64 = 320
3 × 8 = 24
1 × 1 = 1
Total: 320 + 24 + 1 = 345
✔ Answer: 345₁₀
---
12) 1177₈ → ?₁₀
This is 4 digits: positions 3,2,1,0 from left to right? Wait — better to go right to left for powers.
Actually, let’s index from right:
Rightmost digit is position 0.
So:
1 × 8³ = 1 × 512 = 512
1 × 8² = 1 × 64 = 64
7 × 8¹ = 7 × 8 = 56
7 × 8⁰ = 7 × 1 = 7
Wait — that’s if it’s written as 1 1 7 7 from left to right.
Yes:
Digit at position 3 (leftmost): 1 → 1×8³ = 512
Position 2: 1 → 1×8² = 64
Position 1: 7 → 7×8¹ = 56
Position 0: 7 → 7×8⁰ = 7
Sum: 512 + 64 = 576; 576 + 56 = 632; 632 + 7 = 639
✔ Answer: 639₁₀
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13) 415₈ → ?₁₀
4 × 64 = 256
1 × 8 = 8
5 × 1 = 5
Total: 256 + 8 + 5 = 269
✔ Answer: 269₁₀
---
14) 263₈ → ?₁₀
2 × 64 = 128
6 × 8 = 48
3 × 1 = 3
Total: 128 + 48 = 176; 176 + 3 = 179
✔ Answer: 179₁₀
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15) 744₈ → ?₁₀
7 × 64 = 448
4 × 8 = 32
4 × 1 = 4
Total: 448 + 32 = 480; 480 + 4 = 484
✔ Answer: 484₁₀
---
16) 377₈ → ?₁₀
3 × 64 = 192
7 × 8 = 56
7 × 1 = 7
Total: 192 + 56 = 248; 248 + 7 = 255
✔ Answer: 255₁₀
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Final Answer:
1) 212
2) 1344
3) 370
4) 1305
5) 756
6) 1131
7) 440
8) 1372
9) 455
10) 187
11) 345
12) 639
13) 269
14) 179
15) 484
16) 255
Parent Tip: Review the logic above to help your child master the concept of number system conversion worksheet.
