What are the rules for number of sig figs in the answer when multiplying/dividing?

when adding /subtracting?

When multiplying or dividing numbers, the number of significant figures in the answer is determined by the number of significant figures in the original numbers used in the calculation.

- For multiplication: The answer should have the same number of significant figures as the original number with the fewest significant figures.

For example, if you multiply 3.45 by 2.1, the number 3.45 has three significant figures, and the number 2.1 has two significant figures. Therefore, the answer should be rounded to two significant figures, resulting in 7.2.

- For division: Similar to multiplication, the answer should have the same number of significant figures as the original number with the fewest significant figures.

For instance, if you divide 8.25 by 0.0035, the number 8.25 has three significant figures, and the number 0.0035 has two significant figures. The answer should be rounded to two significant figures, resulting in 2,400.

When adding or subtracting numbers, however, the concept of significant figures changes slightly.

- For addition and subtraction: The answer should have the same number of decimal places as the original number with the fewest decimal places.

For example, if you add 2.37 and 4.9, the answer should be rounded to one decimal place since 2.37 has two decimal places and 4.9 has one decimal place. The result would be 7.3.

It is important to note that these rules are used to ensure that the calculated answer reflects the precision of the original measurement or data. By using the appropriate number of significant figures, you can maintain the accuracy of your calculations.