1. Precision, Error and Accuracy Physics 12

2. Measurement  When taking measurements, it is important to note that no measurement can be taken exactly  Therefore, each measurement has an estimate contained in the measurement as the final digit  When taking a measurement, the final digit is an estimate and an error estimate should be included

3. Least Count  When using a measuring device (non-digital) the least count should be determined  The least count is the smallest division that appears on the device (i.e. for a metre stick, it would usually be mm)  When taking a measurement, the digits should be recorded one place past the least count (i.e. for a metre stick, a recording should be to tenths of mm)

4. Digital Devices  Digital devices make the error estimate for you so you will simply record the digits presented on the device  The device should also include an error estimate in the manual or on the label of the device

5. Error Estimate  The error estimate should be for the final digit in a measurement and is commonly ±5  For a meter stick, a measurement would be recorded as 1.5743 ±.0005m

6. Significant Figures  Because all numbers in science are based upon a measurement, the estimates contained in the numbers must be accounted for 1+1=3  While conventional wisdom tells us this is not true, from a science standpoint it could be: 1.4+1.4=2.8

7. Significant Figures  Since the final digit in each measurement is an estimate, we refer to it as an uncertain digit or the least significant digit  This means that any mathematical operation involving this digit in introduces uncertainty to the answer

8. Significant Figures  100.21  +22.436  122.646  In the result of this calculation, there are two uncertain digits  As this does not make sense, the second uncertain digit would be discarded, making the answer 122.65

9. Significant Figures  It is therefore important to know when a digit is significant  A digit is significant if: It is non-zero (i.e. 4246  4SF’s) A zero is between two non-zeros (i.e. 40003  5SF’s) A zero is to the right of the decimal and to the right of a non-zero (i.e. 4.00  3SF’s or 0.00210 3SF’s) All digits in scientific notation (i.e. 3.57x10 3  3SF’s)

10. Significant Figures  The rule that we will use for mathematical operations and significant figures is: Consider all values used in a calculation; the one with the fewest significant figures will determine the number of significant figures in your answer

11. Page 942 (3, 4, 5a, 5b, 6) 3) 3, 2, 3, 2, 3, 1, 3, 7, 1, 2, 4, 4 4) 1.2, 2.3, 5.9, 6.9, 6.3, 4.5, 5.5, 10. 5) 9.7, 290 6) 2.5597x10 0, 1x10 3, 2.56x10 -1, 5.08x10 -5

12. Precision and Accuracy  Precision – describes the exactness and repeatability of a value or set of values. A set of data could be grouped very tightly, demonstrating good precision but not necessarily accuracy  Accuracy – describes the degree to which the result of an experiment or calculation approximates the true value.

13. Precision and Accuracy

14. Error  Random Error Small variations due to randomly changing conditions Repeating trials will reduce but never eliminate Unbiased Affects precision  Systematic Error Results from consistent bias in observation Repeating trials will not reduce Three types: natural, instrument calibration and personal Affects accuracy  There are two types of error that bear consideration following data collection in an experiment.

15. Error Analysis  There are two main calculations that we will use to analyse error in an experiment  Percent Deviation Measures accuracy  Percent Difference Measures precision

16. Review  Page 939 1-5