When working with numbers that have a certain number of significant figures it is often necessary to add or subtract these numbers. When doing so, you must keep track of the number of significant figures that the answer will have.

The rule for addition and subtraction for significant figures is simple:

When quantities are added or subtracted, the number of decimal places in the answer is equal to the number of decimal places in the qunatity with the smallest number of decimal places

For example, if you add 1.23 and 4.567, you get an answer of 5.797. However, 1.23 and 4.567 have different number of decimal places:

1	.	2	3		+
4	.	5	6	7	=
5	.	8	0

Since there is no third decimal place in 1.23, the answer of 5.80 only has two decimal places and thus three significant figures.

You need to be very careful when adding or subtracting numbers in exponential notation that you make sure that the decimal place is in the same place on all the numbers. For example, if you add 1.23*10⁷ and 4.567*10⁶, you should convert one of the numbers so that each has the same exponent: for example, 1.23*10⁷ is also 12.3⁶. Now when you add,

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1	2	.	3			*106	+
	4	.	5	6	7	*106	=
1	6	.	9			*106

Correctly rounded, the answer has only one decimal place and three significant figures.

Example: How many significant figures are there in the answer to the following problem:

4.220*10^-6 - 9.963*10^-7

Solution: The exponents on the numbers are different, so convert one of them to be the same as the other. 9.963*10^-7 is equal to 0.9963*10^-6. Now we can add them:

4	.	2	2	0		*10-6	-
0	.	9	9	6	3	*10-6	=
3	.	2	2	4		*10-6

The answer has three decimal places and four significant figures.

Information provided by: http://learn.chem.vt.edu