Multiplying Decimals Worksheet for students to practice finding the product of decimal numbers.

Sure! Let’s solve each of the 9 decimal multiplication problems step by step. The key rule for multiplying decimals is:

> Multiply as if they were whole numbers, then count the total number of decimal places in both factors — that’s how many decimal places your answer should have.

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🔢 Problem 1: `5.8 × 13`

- Ignore decimals: `58 × 13 = 754`
- Count decimal places: 5.8 has 1 decimal place; 13 has 0
- Total: 1 decimal place
- Answer: 75.4

✔ Answer: 75.4

---

🔢 Problem 2: `6.78 × 0.93`

- Ignore decimals: `678 × 93`

Let’s compute:
```
678
× 93
-----
2034 (678 × 3)
+61020 (678 × 90, shifted one left)
-----
63054
```

- Decimal places: 6.78 → 2, 0.93 → 2 → total 4
- Place decimal: `6.3054`

✔ Answer: 6.3054

---

🔢 Problem 3: `108.73 × 2.18`

- Ignore decimals: `10873 × 218`

This is big — let’s break it down:

First, `10873 × 200 = 2,174,600`
Then, `10873 × 18 = 195,714`
Add: `2,174,600 + 195,714 = 2,370,314`

- Decimal places: 108.73 → 2, 2.18 → 2 → total 4
- Place decimal: `237.0314`

✔ Answer: 237.0314

---

🔢 Problem 4: `496.2 × 3.82`

- Ignore decimals: `4962 × 382`

Compute:

```
4962
× 382
-------
9924 (×2)
396960 (×80, shifted one left)
+1488600 (×300, shifted two left)
-------
1895484
```

- Decimal places: 496.2 → 1, 3.82 → 2 → total 3
- Place decimal: `1895.484`

✔ Answer: 1895.484

---

🔢 Problem 5: `786.27 × 3.3`

- Ignore decimals: `78627 × 33`

Compute:
```
78627
× 33
-------
235881 (×3)
+2358810 (×30, shifted one left)
-------
2594691
```

- Decimal places: 786.27 → 2, 3.3 → 1 → total 3
- Place decimal: `2594.691`

✔ Answer: 2594.691

---

🔢 Problem 6: `999.9 × 7.7`

- Ignore decimals: `9999 × 77`

Compute:
```
9999
× 77
-------
69993 (×7)
+699930 (×70, shifted one left)
-------
769923
```

- Decimal places: 999.9 → 1, 7.7 → 1 → total 2
- Place decimal: `7699.23`

✔ Answer: 7699.23

---

🔢 Problem 7: `128.3 × 2.2`

- Ignore decimals: `1283 × 22`

Compute:
```
1283
× 22
-------
2566 (×2)
+25660 (×20, shifted one left)
-------
28226
```

- Decimal places: 128.3 → 1, 2.2 → 1 → total 2
- Place decimal: `282.26`

✔ Answer: 282.26

---

🔢 Problem 8: `9.8 × 13.8`

- Ignore decimals: `98 × 138`

Compute:
```
98
× 138
------
784 (×8)
2940 (×30, shifted one left)
+ 9800 (×100, shifted two left)
------
13524
```

- Decimal places: 9.8 → 1, 13.8 → 1 → total 2
- Place decimal: `135.24`

✔ Answer: 135.24

---

🔢 Problem 9: `155.72 × 22.7`

- Ignore decimals: `15572 × 227`

This is large — let’s do it carefully.

Break into:
`15572 × 200 = 3,114,400`
`15572 × 20 = 311,440`
`15572 × 7 = 109,004`
Add them:
`3,114,400 + 311,440 = 3,425,840`
`+ 109,004 = 3,534,844`

- Decimal places: 155.72 → 2, 22.7 → 1 → total 3
- Place decimal: `3534.844`

✔ Answer: 3534.844

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## ✔ Final Answers:

| Problem | Answer |
|---------|--------------|
| 1 | 75.4 |
| 2 | 6.3054 |
| 3 | 237.0314 |
| 4 | 1895.484 |
| 5 | 2594.691 |
| 6 | 7699.23 |
| 7 | 282.26 |
| 8 | 135.24 |
| 9 | 3534.844 |

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Let me know if you’d like to see any of these worked out with visual grids or area models! 📐📚