1. Preparation Class for Physics Laboratory
This tutorial is intended to assist students in understanding
Significant Figures and Rounding
Plotting Graphs for Free Fall Experiment
Writing Conclusion

2. Significant Figure Rules
The number of significant figures in a quantity is the number of trustworthy figures in it, the last significant digit in a measurement is somewhat uncertain (but still useful), because it is based upon an estimation.
All non-zero digits are considered significant.
Number
S.F.
The Numbers
123.45 5
1, 2, 3, 4 and 5
523.7  ? ? 
Zeros appearing anywhere between two non-zero digits are significant.
101.12 5
1, 0, 1, 1 and 2.
23.07 ? ? 

3. Significant Figure Rules
Leading zeros are not significant. 2
5 and 2.
5020 ?  ?
0.0500
0.003
800.00
Trailing zeros in a number containing a decimal point are significant. 6
1, 2, 2, 3, 0 and 0.
the zeros before the 1 are not significant
120.00 5 ? 
These conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant.

4. Significant Figure Rules
Examples
Number
Sig. Fig.
23.21 4
0.062 2
275.4
50.09
5020 3
0.003 1
0.0500
800.00 5
1.072
300
300.
300.0
Examples
Operations
Result 17
17.3
9.47 – 2.2
7.3
7.27
8.950 x 10.3
92.2
92.185
/ 6.8
1.8
1.812
Examples
3 ±1 g 1
2.53 ±0.01 g
2.531 ± g
Examples
150.0 g H g salt = g solution
Examples
Quantity
Sig. Fig.
5.2 g 2
5.0 kg
5.000 L 4
0.005 m 1
5.00 x 103 g 3

5. Significant Figure Rules
When numbers are added or subtracted, the number of decimal places in the result should equal to the smallest number of decimal places of any factor in the operation.
makes 17 and NOT
makes and NOT
When multiplying several quantities, the number of significant figures in the final answer is the same as the number of significant figures in the least accurate of the quantities being multiplied.
The same rule is applied to division.
8.950 x 10.3 makes and NOT
/ 6.8 makes and NOT

6. Rounding off
A number is rounded off to the desired number of significant figures by dropping one or more digits to the right. Rules for rounding off are as follows
1) When the first digit dropped is equal to or more than 5, we add 1 to the last digit retained.
e.g. rounding to 3 S.F. makes 6.58
e.g. rounding to 3 S.F. makes 86.3
2) When it is less than 5, the last digit retained does not change.
e.g. rounding to 3 S.F. makes 6.57
Round off the following numbers to 3 S.F.
i = ?
ii = ?
iii x = ? iv v

7. Free Fall Experiment

8. Data of Free Fall Experiment
y(m)
t(s)
5.0
0.88
0.78 10
1.28
1.64 15
1.63
2.68 20
2.18
4.77 25
2.31
5.34

9. Graph Paper

10. Plotting the Axes and Writing their Names & Units

11. Scaling the Axes

12. Plotting Data

13. Best Fit

14. Finding the slope
slope

15. Analyzing
A freely moving object moves with a constant acceleration towards the earth and it obeys the following kinematics equation:
Slope

16. Calculating The Error

17. Random Errors:
A random error, as the name suggests, is random in nature and very difficult to predict. It occurs because there are a very large number of parameters beyond the control of the experimenter that may interfere with the results of the experiment.

18. Example:
You measure the mass of a ring three times using the same balance and get slightly different values: g, g, g

19. How to minimize random errors?
Take more data. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations.

20. Systematic Errors:
Systematic error is a type of error that deviates by a fixed amount from the true value of measurement. All measurements are prone to systematic errors, often of several different types. Sources of systematic error may be imperfect calibration of measurement instruments, changes in the environment which interfere with the measurement process and sometimes imperfect methods of observation.

21. Example:
The cloth tape measure that you use to measure the length of an object had been stretched out from years of use. (As a result, all of your length measurements were too small.)
The electronic scale you use reads 0.05 g too high for all your mass measurements (because it is improperly tared throughout your experiment).

22. How to minimize Systematic Errors?
Systematic errors are difficult to detect and cannot be analyzed statistically, because all of the data is off in the same direction (either to high or too low). Spotting and correcting for systematic error takes a lot of care.
How would you compensate for the incorrect results of using the stretched out tape measure?
How would you correct the measurements from improperly tared scale?

23. Conclusion Part:
Conclusion is an important part of a laboratory report. The main purpose of the conclusion section is to comment on the results mentioned in the lab report so it requires most critical thinking.

24. Discuss the significance of the experiment, think about what you learned!!!

25. When writing your conclusion;
Firstly, restate the purpose of experiment. Briefly state whether your data supported the purpose of the experiment - this would be your conclusion. Discuss whether or not the results supported your hypothesis. If they did not, discuss why not.

26. You can link the results to what you read in the literature, review or other sources mentioned in the introduction. But do not write procedure as your conclusion.

27. Suggest factors that may have affected the experimental design;for instance, random and systematic errors. Discuss how they can be eliminated in the future. Suggest any changes that can be made to the experimental procedure and how these changes might affect the data received in the lab.