### Sig Figs: Addition and Subtraction

Posted:

**Sat Oct 06, 2018 2:10 pm**Hi, I was reading about using sig figs when adding and subtracting and I got confused.

This doesn't make much sense to me, since the digits to the left of the decimal point can also be significant. If you add 12345.6 and 1.008, your final answer would be 12346.6, which has 6 sig figs, even though 1.008 only has 4. Am I making a conceptual error here?

Addition and Subtraction

In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. Let's state that another way: a chain is no stronger than its weakest link. An answer is no more precise that the least precise number used to get the answer. Let's do it one more time: imagine a team race where you and your team must finish together. Who dictates the speed of the team? Of course, the slowest member of the team. Your answer cannot be MORE precise than the least precise measurement.

For addition and subtraction, look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do:

1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.)

2) Add or subtract in the normal fashion.

3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem.

This doesn't make much sense to me, since the digits to the left of the decimal point can also be significant. If you add 12345.6 and 1.008, your final answer would be 12346.6, which has 6 sig figs, even though 1.008 only has 4. Am I making a conceptual error here?