significant figure and rounding data analysis example: data analysis for free fall plotting graph...
TRANSCRIPT
PHYS 101
PREPARATION CLASS FOR PHYSICS LABORATORY
DOĞUŞ ÜNİVERSİTESİ
Significant Figure and Rounding
Data Analysis
Example: “Data Analysis for free fall”
Plotting graph
Writing Conclusion
OUTLINE
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 considered significant
Zeros appearing anywhere between two non-zero digits are significant
Number # of Significant Figure
Significant Figure
12.345 5 1,2,3,4,5
398.5 4 3,9,8,5
85675.2 6 8,5,6,7,5,2
Zero is accepted as a significant figure if there is a significant
figure before it.
If zero comes before the non-zero integer
If zero comes after the non-zero integer
Number # of Significant Figure Significant Figure
3 1 3
0.3 1 3
0.00003 1 3
Number # of Significant Figure Significant Figure
1.0 2 1,0
1.00000 6 1,0,0,0,0,0
0.0100 3 1,0,0
Number # of Significant Figure Significant Figure
50.70 4 5,0,7,0
0.123 3 1,2,3
1.00005 6 1,0,0,0,0,5
Examples:
Number # of Significant Figure Significant Figure
300 1 3
300. 3 3,0,0
300.00 5 3,0,0,0,0
Operations with Significant Figures
Result
153.1+ 12.256 165.356
153.1- 12.256 140.844
153.1* 12.256 1876.3936
153.1/ 12.256 12.49184073
165.4
140.8
1876.
12.49
In addition or subtraction, the result can be as precise as the quantity
with the lowest precision in the operation. Result may have a different
number of significant figures than the inputs.
When we do multiplication or division, the number of significant figures
of the obtained result should be same as the one with the least significant
figures in the operation.
Result with correct SF
Rounding
•A number is rounded off to the desired number of significant figures by dropping one or more digits to the right. When the first digit dropped is equal to or more than 5, we
add 1 to the last digit retained. When it is less than 5, the last digit retained does not change
NumberDesired # of significant
FigureLast Digit
Last Digit smaller,equal or bigger than
5
Rounded number
6.576 3 6 bigger 6.58
86.25 3 5 equal 86.3
6.573 3 3 smaller 6.57
0
0
o
oy
y
v
0oy
g
m5y
m10y
m15y
m20y
m25y
FREE FALL
t0 =0
t1 =0.88 s
t2 =1.28 s
t3 =1.63 s
t4=2.18 s
t5=2.31 s
2
2
1gttvyy oyo
Free fall formulas
0
0
o
oy
y
v
2
2
1gty
22t
yg
Free Fall: Experimental Data
y(m) t(s) t2(s2)
5.0 0.88 0.7810 1.28 1.6415 1.63 2.6820 2.18 4.7725 2.31 5.34
Graph PaperPlotting the axes and Writing their Names & Units
y(m
)
t2 (s2)
Scaling the Axes
0 1 2 3 4 5 6
5
10
15
20
25
y(m
)
t2 (s2)
0 1 2 3 4 5 6
5
10
15
20
25
y(m
)
t2 (s2)
Plotting DataBest Fit
0 1 2 3 4 5 6
5
10
15
20
25
y(m
)
t2 (s2)
0 1 2 3 4 5 6
5
10
15
20
25
y(m
)
t2 (s2)
m .10y
2s 5.2x2m/s 0.4
5.2
.10
x
y
Slope
Slope Of The Graph
Analysis
22t
yg Slope 22
exp m/s 8.0m/s 4.0x 2 erimentalg
Percentage of Error Calculation
x100Error %exp
true
trueerimental
g
gg 19%x100
81.9
81.90.8Error %
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.
Example:You measure the mass of a ring three times using
the same balance and get slightly different values: 17.46 g,
17.42 g, 17.44 g
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.
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
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 previous length measurements would be
smaller than the recent one.)
The electronic scale you use reads 0.05 g too high for all your
mass measurements (because it is improperly tared
throughout your experiment).
How to minimize systematic Errors?
Systematic errors are difficult to detect and cannot be analyzed
statistically, because all the data is off in the same direction (either high
or low).
You can not fix systematic error by repeating the experiment.
Systematic error can be located and minimized with careful analysis
and design of the test conditions and procedure; by comparing your
results to other results obtained independently, using different
equipment or technique
Or by trying out an experimental procedure on a known reference
value, and adjusting the procedure until the desired result is obtained
(this is called calibration).
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.
You should show whether your results are in agreement
with the theoratical values. If not, then you should discuss the
possible reasons for the observed deviation from the
theoretical expectations.
When writing your concluison;Firstly, restate the purpose of the experiment. Discuss the significance of the experiment, think about what you learnedYou can link the results to what you read in the literature, review or other sources mentioned in the introduction. Do not write procedure as your conclusion! Suggest biases 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.
Conclusion Part