1. Topic: Error In the Lab

2. Precision vs. Accuracy  Precision is how closely together measurements agree with each other  0.001 vs 0.1  Accuracy is how close to the accepted value a measurement is  5.50 vs 5.75 (actual is 5.55)

3. Uncertainty  The degree of which you are unsure of your answer is known as the uncertainty.  It can be expressed in two ways:  Whole Value: 15.55 ± 0.05 cm  Percentage: 15.55 ± 3.2% cm  This means that you know the length to be between 15.50 and 15.60

4. Significant Figures  Any non-zero integer is a SIGFIG (1,2,3,4, etc)  123 or 123.5  A captive zero (between two integers) is a SIGFIG  101 or 1.01  A trailing zero (with a decimal) is a SIGFIG  15.590 or 100.0 or 100.  A trailing zero (with no decimal) is NOT  100 or 1050  A leading zero is NOT  0.0005 or 005. or 01

5. Calculations with SIGFIGS  When adding/subtracting SIGFIGS:  Keep the least precise value  2.585 + 1.01 = 3.595 = 3.60  When multiplying/dividing SIGFIGS:  Keep the least TOTAL amount of SIGFIGS  3.45 x 2.5 = 8.625 = 8.6

6. Uncertainty in Measurement  How long would you consider this cylinder to be?  4.5 cm  4.3 cm  4.4 cm  4.35 cm  Now, what’s the uncertainty? Read every gradation, then estimate one more, your uncertainty is half of the estimate. 4.35 ± 0.05 cm

7. Reading a Balance Digital: If measurement is: 14.55 ± 0.01g 14.550 ± 0.001g ONLY for STABLE numbers! Triple Beam Balance: If measurement is: 14.55 ± 0.05g ALWAYS measure to the 100ths

8. Calculating with uncertainties (+, -)  When you add (or subtracting) numbers together with an uncertainty, simply add the uncertainty as well. It should get bigger! (more uncertain)  5.56 ± 0.05 g + 2.50 ± 0.05 g = 8.06 ± 0.10 g

9. Calculating with Uncertainties (x, ÷)  When you multiply (or divide) numbers with an uncertainty, you must add the PERCENTAGE together! (still becoming more uncertain)  10.2 ± 0.5cm x 10.8 ± 0.5cm x 5.5 ± 0.5cm  10.2 ± 4.5% x 10.8 ± 4.6% x 5.5 ± 9.1%  Value: (10.2cm x 10.8cm x 5.5cm) = 605.88 cm 3  Uncertainty: (4.5% + 4.6% + 9.1%) = 18.1 %  605.9 ± 18.1%

10. Percent Error