Measurement

1. Measurement

2. Accuracy vs. Precision

3. Accuracy vs. Precision “Accuracy and precision are really the same thing.” This statement is: true false true in some cases I don’t know, why don’t you tell me?!

4. Accuracy vs. Precision Accuracy describes how close a measurement is to the actual or accepted value. Precisiondescribes how close multiple measurements are to each other.

5. Accuracy vs. Precision An archer shoots six arrows at a target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is: accurate precise both accurate and precise neither accurate nor precise

6. Accuracy vs. Precision The same archer shoots six other arrows at the target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is: accurate precise both accurate and precise neither accurate nor precise

7. Accuracy vs. Precision The archer shoots six more other arrows at the target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is: accurate precise both accurate and precise neither accurate nor precise

8. Accuracy vs. Precision Six more arrows at the target and the results are shown below. If the goal is to hit the “bull’s eye,” then the archer is: accurate precise both accurate and precise neither accurate nor precise

9. Accuracy vs. Precision In summary, (climatica.org.uk) A good measurement is both accurate and precise.

10. Experimental Errors

11. Experimental Errors ALL measurements contain errors! • There are two main types of experimental errors: • systematic errors • random errors

12. Experimental Errors Systematic Errors: • are due to the miscalibration or misuse of a measurement device. • result in a consistently high or low measured value. • affect the accuracy of a measurement. • can usually be eliminated, but are often difficult to detect

13. Experimental Errors Random Errors: • are due to the unpredictable fluctuations in the readings of a measurement device. • could cause the measured value to be higher or lower than the true value. • affect the precision of a measurement. • may be eliminated by averaging multiple measurements.

14. Experimental Errors A student weighs a sample on an electric balance, but forgets to “zero” the balance first causing it to read 0.2 g without anything on it. This is an example of a systematic error. random error. neither (www.alibaba.com)

15. Experimental Errors A multimeter is used to measure the voltage across a resistor in a circuit. The reading fluctuates up and down around 1.5 V. This is an example of a systematic error. random error. neither (learn.sparkfun.com) (minikits.com.au)

16. Experimental Errors A police officer measures the speed of a car three times. The measurements are: 50.1 km/h, 50.4 km/h, and 49.6 km/h This is an example of a systematic error. random error. neither (www.dailymail.co.uk)

17. Experimental Errors The spring in a Newton scale has been stretched beyond it’s elastic limit. When measuring the mass of a 100 g weight, the scale reads 105 g. This is an example of a systematic error. random error. neither (ykonline.yksd.com)

18. Experimental Errors Mr. Lam is trying to time how long it takes a ball to fall to the ground. He pushes the “reset” button on the timer instead of the “start” button. This is an example of a systematic error. random error. neither (www.weiku.com)

19. Significant Figures

20. Significant Figures DoiInthanon – the highest spot in Thailand

21. Significant Figures Since all measurements contain errors, we can not be certain that all of the digits in a measured value are correct. Forexample, a student claims to measure the pencil below to be 6.182 cm. How many of these digits are definitely correct? Probably only two of them!

22. Significant Figures All digits, except the last (rightmost) digit of a significant figure are certain. When reporting measured values, use the rule, “certain, plus one digit” This means that we report all certain digits and also include one uncertain digit. For example, we round the previous measurement to 6.18 m uncertain digit certain digits

23. Significant Figures We call the “certain, plus one” digits of a measurement, “significant figures” or “significant digits.”

24. Significant Figures Does the number of significant figures reflect the accuracy of a measurement or the precision? accuracy precision The more significant there are, the more precise the measurement is.

25. Significant Figures Which significant digits are certain in the following measurements and which are uncertain?

26. Significant Figures How do we know which digits are significant? Memorize the following rules: All non-zero digits are significant. Zeros are significant if: they are between non-zero digits. they are to the right of a decimal AND to the right of non-zero digits. Atlantic Ocean OR use the Pacific-Atlantic “rule”

27. Significant Figures First ask yourself, “is the decimal place present or absent?” Pacific Ocean Atlantic Ocean “Present” “Absent”

28. Significant Figures If the decimal is PRESENT, start on the Pacific side and move along until you reach the first non-zero digit. Pacific Ocean “Present” 13.020

29. Significant Figures Count ALL digits starting from that point. Pacific Ocean “Present” 13.020 Therefore, there are 5 significant figures.

30. Significant Figures Here’s another example. Pacific Ocean Atlantic Ocean “Present” “Absent” 0.00310 Therefore, there are 3 significant figures.

31. Significant Figures If the decimal is ABSENT, start on the Atlantic side and move along until you reach the first non-zero digit. Atlantic Ocean “Absent” 1604

32. Significant Figures Count ALL digits starting from that point. Atlantic Ocean “Absent” 1604 Therefore, there are 4 significant figures.

33. Significant Figures Here’s another example. Pacific Ocean Atlantic Ocean “Present” “Absent” 94200 Therefore, there are 3 significant figures.

34. Significant Figures How many significant figures are there in the following measurement? 43.0 m 1 2 3 4 5

35. Significant Figures How many significant figures are there in the following measurement? 780 m 1 2 3 4 5

36. Significant Figures How many significant figures are there in the following measurement? 0.0078 m 1 2 3 4 5

37. Significant Figures How many significant figures are there in the following measurement? 0.900 m 1 2 3 4 5

38. Significant Figures How many significant figures are there in the following measurement? 9046 m 1 2 3 4 5

39. Significant Figures How many significant figures are there in the following measurement? 1000 m 1 2 3 4 5

40. Significant Figures How many significant figures are there in the following measurement? 1000.0 m 1 2 3 4 5

41. Significant Figures How many significant figures are there in the following measurement? 6010 m 1 2 3 4 5

42. Operations with Significant Figures

43. Adding and Subtracting RULE: The answer should have the same number of decimal placesas the measurement with the least number of decimal places. Example 310.4 + 46.280 1 decimal place round to 1 decimal place 3 decimal places 356.680 356.7 certain digit + uncertain digit = uncertain digit

44. Multiplying and Dividing RULE: The answer should have the same number of significant figuresas the measurement with the least number of significant figures. Example 310.4 x 46.280 4 significant figures round to 4 significant figures 5 significant figures 14365.312 14370 Multiplying or dividing can not increase the number of significant figures!