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Physics 2149 Lecture 01
Significant figures
1)
The number of digits used to express a quantity is an implicit indication of the uncertainty of the value.
a)
As a rough estimate of the uncertainty we will assume that the measurement is good to within ±1 of
the last significant digit recorded.
b)
Example 1.1:
The length of a beam is measured as L = 5.5 m.
What is the implicit range of values
this measurement could take?
A rough estimate of the uncertainty in the measurement would be:
5.4
5.6
mL
m
≤≤
2)
Rules for determining the number of significant figures:
a)
All non zero digits are counted.
b)
Zeros are only counted if
i)
they appear between two or more non zero digits
ii)
they appear after a decimal place at the end of a number
3)
Example 1.2:
Value
# of Sig. Figs.
Value
# of Sig. Figs.
308.02
5
3.000
4
0.0033
2
8600
2
0.0330
3
3
8.600 10
×
4
4)
General Rule for zeros:
Zeros are not counted if they can be replaced by powers of ten.
5)
Writing your values in scientific notation can remove any confusion about the number of significant
figures
Value
scientific notation
Value
scientific notation
308.02
2
3.0802 10
×
3.000
3.000
0.0033
3
3.3 10
−
×
8600
3
8.6 10
×
0.0330
2
3.30 10
−
×
3
8.600 10
×
8.600 3
E
6)
IMPORTANT:
When doing the web assignments you must use the “E” method of scientific notation.
a)
Example 1.3:
How would you express 0.015 to 3 significant figures on a web assignment?
1.50
2
E
−
7)
Rules for addition and subtraction
a)
round of the answer to the same number of
decimal places
as the value with the least number of
decimal places
b)
Example 1.4:
What is 83.624 – 3.51?
83.624
(3 decimal places)
3.51
(2 decimal places)
80.114
(3 decimal places)
−
This must rounded to 2 decimal places so the final answer is 80.11.
8)
Rules for multiplication and division
a)
round the answer to the same number of
significant figures
as the value with the least number of
significant figures.
b)
Example 1.5:
What is 636.82 × 1.1?
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636.82
(5 significan figures)
1.1
(2 significan figures)
700.502
(6 significan figures)
×
This must be rounded to 2 significant figures so the answer is
2
7.0 10
×
c)
Example 1.6:
The length of a slab is measured to be 25 m.
The width is measured to be 5 m.
Roughly what is the surface are of the slab? 100 m
2
.
Explicit Uncertainties
1)
When possible it is preferable to state explicitly the possible range within which a measured value
probably lies. eg.
The length of a beam is measured as
5.5 0.1
L
m
=
±
2)
Uncertainty
()
u
Δ
:
a statement that defines the range within which the “true” measurement will be
found.
3)
Accuracy
a
Δ
:
corresponds to how well the instrument has been calibrated against the accepted
standard measurements.
a)
The manufacturer tells you what the accuracy of the instrument is.
4)
Precision
p
Δ
:
corresponds to the uncertainty that you feel you have when you use the instrument.
There may be two parts to this:
a)
Instrument precision:
what is the smallest division you can read on the instrument?
Usually ½ the
smallest division is a good estimate of the instrument precision.
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 Spring '11
 blamculeam
 Physics

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