Decimal to Binary Conversion Worksheet for 8th - 10th Grade ... - Free Printable

It looks like you've uploaded a worksheet titled "Decimal to Binary Conversion Worksheet" from math-worksheet.org, which asks you to convert decimal numbers into their binary equivalents.

Here is the list of decimal numbers that need to be converted:

1. 55
2. 147
3. 227
4. 295
5. 217
6. 252
7. 122
8. 109
9. 215
10. 41

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🔧 How to Convert Decimal to Binary

To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainder. The binary representation is the sequence of remainders read from bottom to top.

Let’s go through each one step-by-step.

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#### 1. 55
- 55 ÷ 2 = 27 rem 1
- 27 ÷ 2 = 13 rem 1
- 13 ÷ 2 = 6 rem 1
- 6 ÷ 2 = 3 rem 0
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Reading remainders from bottom to top: 110111

✔ 55 = 110111₂

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#### 2. 147
- 147 ÷ 2 = 73 rem 1
- 73 ÷ 2 = 36 rem 1
- 36 ÷ 2 = 18 rem 0
- 18 ÷ 2 = 9 rem 0
- 9 ÷ 2 = 4 rem 1
- 4 ÷ 2 = 2 rem 0
- 2 ÷ 2 = 1 rem 0
- 1 ÷ 2 = 0 rem 1

Remainders: 10010011

✔ 147 = 10010011₂

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#### 3. 227
- 227 ÷ 2 = 113 rem 1
- 113 ÷ 2 = 56 rem 1
- 56 ÷ 2 = 28 rem 0
- 28 ÷ 2 = 14 rem 0
- 14 ÷ 2 = 7 rem 0
- 7 ÷ 2 = 3 rem 1
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Remainders: 11100011

✔ 227 = 11100011₂

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#### 4. 295
- 295 ÷ 2 = 147 rem 1
- 147 ÷ 2 = 73 rem 1
- 73 ÷ 2 = 36 rem 1
- 36 ÷ 2 = 18 rem 0
- 18 ÷ 2 = 9 rem 0
- 9 ÷ 2 = 4 rem 1
- 4 ÷ 2 = 2 rem 0
- 2 ÷ 2 = 1 rem 0
- 1 ÷ 2 = 0 rem 1

Remainders: 100100111

✔ 295 = 100100111₂

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#### 5. 217
- 217 ÷ 2 = 108 rem 1
- 108 ÷ 2 = 54 rem 0
- 54 ÷ 2 = 27 rem 0
- 27 ÷ 2 = 13 rem 1
- 13 ÷ 2 = 6 rem 1
- 6 ÷ 2 = 3 rem 0
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Remainders: 11011001

✔ 217 = 11011001₂

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#### 6. 252
- 252 ÷ 2 = 126 rem 0
- 126 ÷ 2 = 63 rem 0
- 63 ÷ 2 = 31 rem 1
- 31 ÷ 2 = 15 rem 1
- 15 ÷ 2 = 7 rem 1
- 7 ÷ 2 = 3 rem 1
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Remainders: 11111100

✔ 252 = 11111100₂

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#### 7. 122
- 122 ÷ 2 = 61 rem 0
- 61 ÷ 2 = 30 rem 1
- 30 ÷ 2 = 15 rem 0
- 15 ÷ 2 = 7 rem 1
- 7 ÷ 2 = 3 rem 1
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Remainders: 1111010

✔ 122 = 1111010₂

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#### 8. 109
- 109 ÷ 2 = 54 rem 1
- 54 ÷ 2 = 27 rem 0
- 27 ÷ 2 = 13 rem 1
- 13 ÷ 2 = 6 rem 1
- 6 ÷ 2 = 3 rem 0
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Remainders: 1101101

✔ 109 = 1101101₂

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#### 9. 215
- 215 ÷ 2 = 107 rem 1
- 107 ÷ 2 = 53 rem 1
- 53 ÷ 2 = 26 rem 1
- 26 ÷ 2 = 13 rem 0
- 13 ÷ 2 = 6 rem 1
- 6 ÷ 2 = 3 rem 0
- 3 ÷ 2 = 1 rem 1
- 1 ÷ 2 = 0 rem 1

Remainders: 11010111

✔ 215 = 11010111₂

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#### 10. 41
- 41 ÷ 2 = 20 rem 1
- 20 ÷ 2 = 10 rem 0
- 10 ÷ 2 = 5 rem 0
- 5 ÷ 2 = 2 rem 1
- 2 ÷ 2 = 1 rem 0
- 1 ÷ 2 = 0 rem 1

Remainders: 101001

✔ 41 = 101001₂

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✔ Final Answers:

| Decimal | Binary |
|--------|------------|
| 55 | 110111 |
| 147 | 10010011 |
| 227 | 11100011 |
| 295 | 100100111 |
| 217 | 11011001 |
| 252 | 11111100 |
| 122 | 1111010 |
| 109 | 1101101 |
| 215 | 11010111 |
| 41 | 101001 |

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