If the number 481*673 is completely divisible by 9, then the smallest whole…

Step-by-Step Solution

To determine the smallest whole number that can replace the asterisk () in the number 481673 so that it is completely divisible by 9, we apply the divisibility rule for 9.

1. Apply the Divisibility Rule for 9: A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

2. Calculate the sum of the known digits: The known digits are 4, 8, 1, 6, 7, and 3. Sum = 4 + 8 + 1 + 6 + 7 + 3 = 29.

3. Formulate the equation: Let the missing digit be x. The sum of all digits is 29 + x. For the number to be divisible by 9, 29 + x must be a multiple of 9 (e.g., 9, 18, 27, 36...).

4. Solve for x:

   • If 29 + x = 36, then x = 36 - 29 = 7.

   • Since 7 is a whole number, it is the smallest digit that satisfies the condition.