Number of Significant Figures in Result of Addition or Subtraction

Theorem
Let $m$ and $n$ be numbers.

Let $d_m$ and $d_n$ be the position of the least significant digit of $m$ and $n$ respectively.

Then the least significant digit in either $m + n$ or $m - n$ is in the position corresponding to the greater significant digit of $d_m$ and $d_n$.