1. Precision, Error and Accuracy Physics 12 Adv

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. 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.

12. Precision and Accuracy

13. 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: natrual, instrument calibration and personal Affects accuracy  There are two types of error that bear consideration following data collection in an experiment.

14. 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

15. 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.

16. Precision and Accuracy

17. 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: natrual, instrument calibration and personal Affects accuracy  There are two types of error that bear consideration following data collection in an experiment.

18. 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