Significant Figures/Accuracy and Precision
Feb 24, 2016
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!