Starter 1.How would you record the following measurements? How many sig figs? a.b. 2.Count the sig figs in the following measured values: a b.1890 c d x 10 6 mL inches

Starter Answers 1.How would you record the following measurements? How many sig figs? a.b. 2.Count the sig figs in the following measured values: a sig figs b sig figs c sig figs d x sig figs 4.98 mL 3 sig figs 8.24 in 3 sig figs mL inches Your last digit might be different!

Arithmetic with Significant Figures 

Arithmetic with sig figs! Sometimes we need to use our measured values in calculations. Here are some examples:

When you do arithmetic, you need to figure out how many sig figs your answer should have. This will depend on the sig figs in your measurements. Remember, your measurements might have been made with different amounts of precision. This is reflected by the number of sig figs. Low precision in one measurement will limit the precision of your answer. Arithmetic with sig figs!

Example Let’s say you wanted to calculate the density of a liquid. To do this, you found the volume using a beaker. The volume was 55 mL. Then, you used an analytical balance to measure the mass. The mass was g. How precise is the answer? How many sig figs should I record? 6 sig figs 2 sig figs 1.0 g/mL 2 sig figs

Multiplication and Division The general rule for multiplication and division is that your answer must have only as many sig figs as the least precise measurement. Example 2 sig figs 4 sig figs 13 m 3 Round to 2 sig figs 3 sig figs

More Example

4 sig figs3 sig figs 2 sig figs 1 sig fig 2 sig figs5 sig figs 1 sig fig 2 sig figs

Addition and Subtraction The rules for addition and subtraction are different. For addition and subtraction the answer must be rounded to the least number of decimal places from any of the terms. 2 decimal places 1 decimal place Round to 1 decimal place 5.9 mL

Examples

Answers 2 decimal places3 decimal places 2 decimal places 0 decimal places1 decimal place 0 decimal places 2 decimal places1 decimal place 3 decimal places2 decimal places