Significant Figures/Accuracy and Precision

Accuracy =

Precision =

Accuracy vs PrecisionHow close you are to the correct answer

How close your answers are to each other

You can quantify how accurate you are by calculating the percent error of your measurement

Percent Error = Experimental Value – Accepted Value x 100 Accepted Value

Absolute Value Sign – Make this value positive

Percent Error

In the lab, you measure the mass of an object to be 3.56 g. The actual mass of the object is 4.23 g. What is the percent error?

Percent Error = Experimental Value – Accepted Value x 100 Accepted Value

Percent Error = 3.56g – 4.23g x 100 = 15.8% 4.23

Example

When you record a measurement, always record all certain digits PLUS one uncertain digit.

These are called the significant figures (digits) of the measurement

Measurement

If the measurement lands on a line, the uncertain number is 0!

0.90 cm

Measurement

Rules for Identifying Significant Figures (Sig Figs)(Found on your STAAR Reference Sheet)

1. Non-zero digits and zeros between non-zero digits are always significant. 145 (3 s.f.) , 2001 (4 s.f.)

2. Leading zeros are not significant. 0.00032 (2 s.f.)

3. Zeros to the right of all non-zero digits are only significant if a decimal point is shown.

3.400 (4 s.f.), 200 (1 s.f.)

Sig Fig Rules

Determine the number of sig. figs. in the following numbers.

Practice!2sf4sf

2sf

2sf

4sf

0.00323200

32.00 3002

32

Rounding multiplication/division calculationsto the proper number of sig figs

Round the answer to the lowest number of sig figs in the calculation

23.0 x 2.003 x 0.245 = 11.286905 = 3sf 4sf 3sf

Mult./Div. Rules

11.33 sf

Perform the following calculations and round the answer to the proper number of sig figs.

450 = 3.947368421 = 114

84 x 31.221 = 2622.564 =

Practice!2 sf 2 sf

3.9

3 sf

2 sf 5 sf 2 sf

2600

Rounding addition/subtraction calculationsto the proper number of decimals

Round the answer to the lowest number of decimals (dp) in the calculation

23.0 + 2.003 + 0.24 = 25.243 =

Add./Sub. Rules

25.21 dp1 dp 3 dp 2 dp

Perform the following calculations and round the answer to the proper number of decimal places.

39.64 + 1.3 = 40.94 =

195.4 - 193 = 2.4 =

Practice!1 dp1 dp2 dp

1 dp 0 dp 0 dp

2

40.9

Finished!