Work out the
`12.8xx1.5xx2.3`

Answer

To solve the problem \( 12.8 \times 1.5 \times 2.3 \), we will follow these steps:

### Step 1: Multiply 12.8 and 1.5

1. **Set up the multiplication**:
- Write the numbers one below the other:
```
12.8
× 1.5
```

2. **Multiply the digits**:
- Start with the digit in the tenths place of 1.5 (which is 5):
- \( 5 \times 8 = 40 \) (write down 0 and carry over 4)
- \( 5 \times 2 = 10 \), plus the carry 4 gives \( 14 \) (write down 4 and carry over 1)
- \( 5 \times 1 = 5 \), plus the carry 1 gives \( 6 \)

- Now, write the result:
```
12.8
× 1.5
--------
64.0 (This is from multiplying by 5)
```

3. **Multiply the next digit (1)**:
- Multiply by the digit in the ones place of 1.5 (which is 1):
- \( 1 \times 8 = 8 \)
- \( 1 \times 2 = 2 \)
- \( 1 \times 1 = 1 \)

- Write this down, shifted one place to the left:
```
12.8
× 1.5
--------
64.0
+ 12.8 (This is from multiplying by 1)
```

4. **Add the results**:
- Now add the two results together:
```
64.0
+ 12.8
--------
76.8
```

5. **Place the decimal**:
- Since we multiplied one number with one decimal place and the other with one decimal place, we have a total of 2 decimal places. Thus, the result is \( 76.8 \).

### Step 2: Multiply the result with 2.3

1. **Set up the multiplication**:
- Now we will multiply \( 76.8 \) by \( 2.3 \):
```
76.8
× 2.3
```

2. **Multiply the digits**:
- Start with the digit in the tenths place of 2.3 (which is 3):
- \( 3 \times 8 = 24 \) (write down 4 and carry over 2)
- \( 3 \times 6 = 18 \), plus the carry 2 gives \( 20 \) (write down 0 and carry over 2)
- \( 3 \times 7 = 21 \), plus the carry 2 gives \( 23 \)

- Write the result:
```
76.8
× 2.3
--------
230.4 (This is from multiplying by 3)
```

3. **Multiply the next digit (2)**:
- Now multiply by the digit in the ones place of 2.3 (which is 2):
- \( 2 \times 8 = 16 \) (write down 6 and carry over 1)
- \( 2 \times 6 = 12 \), plus the carry 1 gives \( 13 \) (write down 3 and carry over 1)
- \( 2 \times 7 = 14 \), plus the carry 1 gives \( 15 \)

- Write this down, shifted one place to the left:
```
76.8
× 2.3
--------
230.4
+153.6 (This is from multiplying by 2)
```

4. **Add the results**:
- Now add the two results together:
```
230.4
+153.6
--------
176.64
```

5. **Place the decimal**:
- Since we multiplied two numbers with one decimal place each, we have a total of 2 decimal places. Thus, the result is \( 176.64 \).

### Final Answer
The final result of \( 12.8 \times 1.5 \times 2.3 \) is \( 44.16 \).