1. 1 Error VS Mistakes Error may occur every time you make a measurement in an experiment. A mistake is a blunder or unintentional action whose consequence is not desirable. Error, on the other hand, accounts for the range of values that are normally obtained from successive measurements of the same quantity, even though there was no perceived mistake in any of the measurements.

2. 2 Error & Precision & Accuracy Error is closely related to precision. Precision is a term that refers to the agreement between successive measurements of the same quantity. Precision is not related to accuracy because accuracy refers to the agreement between a measured value of a quantity and its true value. In cases in which it is not possible to know the true value of a quantity, it is impossible to know the accuracy of the measurement. However, it is always possible to judge the precision of a measured value by making more than one measurement.

3. 3 Example For example, suppose we measured the mass of an object during two successive trials and found values of 3.6342 g and 3.6344 g. Since there is obviously close agreement, we have achieved very good precision. Alternatively, suppose we found 3.6342 g in the first measurement and 3.5671 g in the second measurement. You can see that good precision is lacking because close agreement has not been achieved. Consider another aspect of this data. Would we be justified in reporting the mass as 3.6342 g? Would it be better to report 3.5671 g? Could we say at least that the mass lies between 3.5 g and 3.6 g? How can we report our measurements in a way that reflects their precision?

4. The “Undesirable” situation Rounding Twice within the same problem. The intermediate answer is rounded with one extra digit (the first insignificant digit) The “incorrectly” rounded intermediate answer (has one too many digits) is carried through in the calculation but then the answer is rounded according to the “correct” sig. figs.

5. Example (17000 + 256)/ 3.5782 (42.38 + 7.745)/(78.44 – 27.423)

6. Mulitiplication by a Small Whole Number (exact number) Two ways to go: 1. Treat the problem as a simple multiplication problem. 2. Treat the problem as an addition problem and then rounding using addition/subration rule.

7. Example 3 identical coins weigh 6.32g each. What is the total mass? 3 x 6.32 = OR 6.32 + 6.32 + 6.32 =

8. Where they are both have the same sig figs. 3 x 19.13 = 57.39 And 19.13 + 19.13 + 19.13 = 57.39

9. Uncertainty and Scientific Notation 4.200 x 10 4 = 10 -3 x 10 4 = 10 1 ( +- 10) 4.2 x 10 5 4.2 x 10 -1 4.2 X 10 -3