1. Chapter 3 Experimental Error

2. Significant Figures Significant Figures are the minimum number of digits required to express a value in scientific notation without loss of accuracy. 16 meters 0.001320 cm 93,000,000 miles 1021 liters 30.0 grams

3. Measure as accurately as possible Read all graduations Estimate a last place, this last place is significant but uncertain. Integers have no uncertainty.

4. Rules (Addition and Subtraction) Governed by uncertain position. Round all digits to be discarded. Only carry out on final answer. How far is it from here to Boston?

5. Rules (Multiplication and division) Governed by number with least number of significant figures. 1.7cm x 34.54cm x 87.123cm = 4671.361014 cm 3 = 4.7x10 2 cm 3 Volume of a sheet of paper

6. Rules (logs) n = 10 a means log n = a log 1948 = 3.2896 Red is characteristic Green is mantissa Mantissa has the proper number of significant figures. So 10 3.2896 = 1948

7. Question A solution has a pH of 5, how many significant figures? Be very careful with logs. They do not follow the same math rules a regular numbers. If you were to want to average the pH of two lakes then using the normal way we calculate a mean gives us a number of dubious value. Thought experiment – take 100 mL of a pH 1.00 solution and add it to 100 mL of a pH 3 solution. What is the new pH?

8. Errors Systematic or determinate error Random or indeterminate error

9. Precision and accuracy Precision – ability to reproduce a result Accuracy – closeness to the true value Can be absolute or relative Relative is error/value Can be pph, ppt, ppm

10. Four Possibilities

11. Red is the location of the pellet (On the average the duck was dead!)

12. Propagation of uncertainty Addition and Subtraction Multiplication and Division re is relative error. This could be percent if you like but I view that as an added calculation that you don’t really need