I have learned in class that to subtract decimal numbers and keep significant figures, one just lines up the decimal, then rounds the answer according to the operand with the fewest places after the decimal.
My question is how to handle an integer subtracted by a decimal.
112 - 12.0
If I add the decimal to 112.0, my concern comes with 100.0 being 4 significant figures, which has more than either of the original operands.
When adding or subtracting, you don't count significant figures, you round to the least accurate. Your $112$ could be anywhere in $(111.5,112.5)$, so knowing that the $12.0$ is in $(11.95,12.05)$ is not much better than knowing it is in $(11.5,12.5)$. You should report your result as $100$, using whatever notation you have to show that the last zero (the one's place) is significant. What you really know is that the difference is in $(99.45,100.55)$, which could round away from $100$, but it is not likely.
Of $112$ and $12.0,$ $112$ is less precise, since $12.0$ is significant to $10^{-1}$ while $112$ is significant only to $10^0.$ So the difference is significant only to the $10^0$ place.
So $112 - 12.0 = 100.$ where the decimal after the $100$ indicates that you know $100$ to three significant figures.
Writing the numbers in scientific notation removes any doubt. The expression with the correct number of significant figures is $1.00 \times 10^2.$ It's clear that you're dealing with three significant figures in this case.
