The unit digit of the sum of the first 111 whole numbers is 5.

Quick Scoop: Final Answer

We are summing the first 111 whole numbers:
0+1+2+3+⋯+1100+1+2+3+\dots +1100+1+2+3+⋯+110. This is the same as the sum of the first 110 natural numbers, since adding 0 does nothing to the sum. The sum of the first nnn natural numbers is:

S=n(n+1)2S=\frac{n(n+1)}{2}S=2n(n+1)​

Here n=110n=110n=110, so:

S=110×1112=55×111S=\frac{110\times 111}{2}=55\times 111S=2110×111​=55×111

To get the unit digit , we only care about the unit digits of the factors:

  • Unit digit of 55 → 5
  • Unit digit of 111 → 1

Now multiply unit digits:

5×1=55\times 1=55×1=5

So, the unit digit of the sum is 5.