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Errro AnalysisError
Why Bother?
• The knowledge we have of the physical world is obtained by doing experiments and making measurements.
• It is important to understand how to express such data and how to analyze and draw meaningful conclusions from it.
Why Bother?
• ALL measurements of physical quantities are subject to uncertainties.
• It is never possible to measure anything exactly.
• in order to draw valid conclusions the error must be indicated and dealt with properly.
Example: Your Height is 5' 8“. How accurate is this?
The height of a person depends on :• how straight she stands, • Did she just got up from lying horizontally • Did she has her shoes on• How long her hair is • How her hair is made up. • A quantity such as height is not exactly
defined without specifying many other circumstances.
That’s Not All…..
• Even if you could precisely specify the "circumstances," your result would still have an error associated with it.
• The scale you are using is of limited accuracy • when you read the scale, you may have to
estimate a fraction between the marks on the scale, etc.
The two essential components of a physical measurement
• (1) A numerical value (in a specified system of units) giving the best estimate possible of the quantity measured
• (2) the degree of uncertainty associated with this estimated value.
• For example, a measurement of the width of a table would yield a result such as
• 95.3cm +/- 0.1 cm.
Significant Figures
• Definition: The significant figures of a quantity are the meaningful digits in it.
• 1. Any digit that is not zero is significant.
549 1.892
Significant Figures
• 2. Zeros between non zero digits are significant.
• 4023• 68907• 101
Significant Figures
• 3. Zeros to the left of the first non zero digit are not significant
• 0.000034 = 3.4x10-5 • 0.01 = 1x10-2 • 0.00416 = 4.16x10-3
Significant Figures
• For numbers with decimal points, zeros to the right of a non zero digit are significant.
• 2.00 has three significant figures • 0.050 has two significant figures. • For this reason it is important to keep the
trailing zeros to indicate the actual number of significant figures.
Percent Error
• To express the magnitude of the error (or deviation) between two measurements scientists invariably use percent error .
Order of Magnitude
• Used to make a rough comparison between compare numbers.
• Order of Magnitude of 1 = 101
• Order of Magnitude of 2 = 102
• Order of Magnitude of 3 = 103 etc.
How to Find the Order of Magnitude of a number
• Write the number in Scientific Notation• If the mantissa (left side) is greater than 5, then go up
one more power. • Example: 8.9 x 104
It is greater than 5.0x104 Therefore 8.9x 104 would have an Order of Magnitude of 5.
• **check: 89,000 is closer to 100,000 • than 10,000.
Order of Magnitude Number Scientific
NotationGreater than 5 In the mantissa
Order of Magnitude
2789 2.789x103 No 3
5510 5.510 x 103 Yes 4
97000 9.7000 x 104
0.00678 6.78 x 10-3
0.00456 4.56 x 10-3