To find the product of 73.458 and 0.39, we will perform a multiplication. To carry out this calculation by hand, we will follow these steps:
1. Ignore the decimals for a moment and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in both the numbers.
3. Place the decimal in the product so that the total number of decimal places in it is equal to the sum obtained in step 2.
Step 1: Multiplying as whole numbers
First, multiply 73458 (73.458 without the decimal) and 39 (0.39 without the decimal):
```
73458
× 39
-------
66114 (73458 × 9)
+293832 (73458 × 3, but shifted one place to the left, as it is actually 30)
-------
```
Now, we will add 66114 and 293832 (shifted one place to the left):
```
66114
293832
-------
2864934
```
The result of the multiplication without considering the decimal places is 2864934.
Step 2: Counting decimal places
The number 73.458 has three decimal places, and the number 0.39 has two decimal places. So, in total, we have:
3 (from 73.458) + 2 (from 0.39) = 5 decimal places.
Step 3: Placing the decimal
Since our result should have 5 decimal places, we start from the right of our product and count five places to the left. After counting, we place the decimal point there:
Product without the decimal: 2864934
After placing the decimal (5 places from the right): 28.64934
So, the product of 73.458 and 0.39 is 28.64934.
This is the value that should go in the empty box to complete the calculation for the multiplication of these two numbers.