What should be the missing digit so that the number 275_476 becomes exactly divisible by 11?

Let the missing digit be k. The number is 275k476.
According to the divisibility rule of 11, the difference between the sum of digits at odd positions and the sum of digits at even positions must be either 0 or a multiple of 11.

Let's label the positions from right to left (or left to right):
Digits at odd positions (1st, 3rd, 5th, 7th from left): 2,5,4,6

Sum of odd position digits=2+5+4+6=17
Digits at even positions (2nd, 4th, 6th from left): 7,k,7

Sum of even position digits=7+k+7=14+k
Now, compute the difference:

Difference=17−(14+k)=3−k
For the number to be divisible by 11, this difference must be 0 (since k is a single-digit integer from 0 to 9):

3−k=0
k=3