Worksheet for converting decimal numbers to binary.

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 remainders read from bottom to top.

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

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✔ 1. 55 → Binary

```
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
```

Read remainders from bottom to top: 110111

✔ 55₁₀ = 110111₂

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✔ 2. 147 → Binary

```
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

✔ 147₁₀ = 10010011₂

---

✔ 3. 227 → Binary

```
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

✔ 227₁₀ = 11100011₂

---

✔ 4. 295 → Binary

```
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

✔ 295₁₀ = 100100111₂

---

✔ 5. 217 → Binary

```
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

✔ 217₁₀ = 11011001₂

---

✔ 6. 252 → Binary

```
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

✔ 252₁₀ = 11111100₂

---

✔ 7. 122 → Binary

```
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

✔ 122₁₀ = 1111010₂

---

✔ 8. 109 → Binary

```
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

✔ 109₁₀ = 1101101₂

---

✔ 9. 215 → Binary

```
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

✔ 215₁₀ = 11010111₂

---

✔ 10. 41 → Binary

```
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

✔ 41₁₀ = 101001₂

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📝 Final Answer Table

| 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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You can now fill in the blanks on your worksheet with these binary values!

Let me know if you'd like this in a printable format or need help understanding the process further!