To solve the multiplication of 23.71 and 2.34 step by step, follow these instructions:
### Step 1: Write the numbers in a column format
Align the numbers for multiplication:
```
23.71
× 2.34
```
### Step 2: Multiply the first digit of the bottom number (4) by the top number (23.71)
Multiply 23.71 by 4:
- 4 × 1 = 4
- 4 × 7 = 28 (write down 8, carry over 2)
- 4 × 3 = 12, plus the carry 2 = 14 (write down 4, carry over 1)
- 4 × 2 = 8, plus the carry 1 = 9
So, the first row of the multiplication gives us:
```
9484
```
### Step 3: Multiply the second digit of the bottom number (3) by the top number (23.71)
Now, multiply 23.71 by 3, remembering to shift one position to the left:
- 3 × 1 = 3
- 3 × 7 = 21 (write down 1, carry over 2)
- 3 × 3 = 9, plus the carry 2 = 11 (write down 1, carry over 1)
- 3 × 2 = 6, plus the carry 1 = 7
So, the second row of the multiplication gives us:
```
7113 (shifted one position to the left)
```
### Step 4: Multiply the third digit of the bottom number (2) by the top number (23.71)
Now, multiply 23.71 by 2, remembering to shift two positions to the left:
- 2 × 1 = 2
- 2 × 7 = 14 (write down 4, carry over 1)
- 2 × 3 = 6, plus the carry 1 = 7
- 2 × 2 = 4
So, the third row of the multiplication gives us:
```
4742 (shifted two positions to the left)
```
### Step 5: Add all the rows together
Now, we add all the rows together:
```
9484
+ 71130
+ 474200
__________
554814
```
### Step 6: Place the decimal point
Count the total number of decimal places in the original numbers:
- 23.71 has 2 decimal places
- 2.34 has 2 decimal places
Total = 2 + 2 = 4 decimal places.
So, we place the decimal point in 554814 to get:
```
55.4814
```
### Final Answer
Thus, the result of multiplying 23.71 by 2.34 is **55.4814**.
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