Starter1. How would you record the following measurements? How many

sig figs?a. b.

2. Count the sig figs in the following measured values:a. 0.0004050b. 1890c. 1890.090d. 6.930 x 106

mL

inches

Starter Answers1. How would you record the following measurements? How many

sig figs?a. b.

2. Count the sig figs in the following measured values:a. 0.0004050 4 sig figsb. 1890 3 sig figsc. 1890.090 7 sig figsd. 6.930 x 106 4 sig figs

4.98 mL3 sig figs

8.24 in3 sig figs

mL

inchesYour 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:

hwlVolume

mmmMassAve

VVVolumeDisplacedt

ds

V

md

fi

3

)(. 321

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!

ExampleLet’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 55.1345 g.

mL

g

V

md

55

1345.55

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 DivisionThe general rule for multiplication and division is that your answer must have only as many sig figs as the least precise measurement.

Example2 sig figs

4 sig figs

13 m3

Round to2 sig figs

mmmhwlVolume 56.4335.22.1

3 sig figs

More Example

4200.800

500012.012465

0123.0465.3

More Example

194200.800

3500012.012465

2820123.0465.3

4 sig figs 3 sig figs 3 sig figs

3 sig figs 2 sig figs 2 sig figs 1 sig fig

2 sig figs5 sig figs

1 sig fig

2 sig figs

Addition and SubtractionThe 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.

mLmLVolumeDisplaced 1.801.14

2 decimal places

1 decimal placeRound to1 decimal place

5.9 mL

Examples

02.0341.97

0.401.0

2.112

152.083.9

Answers

32.9702.0341.97

0.40.401.0

112.112

98.9152.083.9

2 decimal places 3 decimal places

2 decimal places

0 decimal places 1 decimal place

0 decimal places

2 decimal places 1 decimal place

1 decimal place

3 decimal places 2 decimal places2 decimal places