Numbers
Scientific Notation
In physics numbers can be very large and very small.
Scientific notation uses powers of 10 to represent
decimal places.
• Positive powers for large numbers: 456000 = 4.56 x 105
• Negative powers for small numbers: 0.00753 = 7.53 x 10-3
Write a number in scientific notation with only one
non-zero value to the left of the decimal place.
Order of Magnitude
You 5’9” = 1.75 m ≈ 100 m
Lecture Hall 14 m ≈ 101 m
Faraday West 80 m ≈ 102 m
NIU 2000 m ≈ 103 m
Each of these lengths is different by about one
order of magnitude
Map Lengths
Huskie Stadium 100 m ≈ 102 m
DeKalb City 4 km = 4000 m ≈ 103 m
DeKalb County 30 km = 30,000 m ≈ 104 m
Illinois 400 km ≈ 105 m
mapquest uses scaling factors, about two
steps per order of magnitude
Uncertainty
A student measures a length of 50.0 cm with a
meterstick divided with marks at each millimeter. The
uncertainty is about
A) 0.5 cm
B) 0.5 %
C) 0.2 %
D) 0.02
E) 0.1
Accuracy
The smallest unit on a measuring device sets the
accuracy.
In general, a measurement is only as accurate as the
smallest unit.
Significant figures are a guide to the accuracy of a
measurement.
Significant Figures
Any value is expressed in some number of digits.
The number of digits (without left side zeroes) is the
number of significant figures.
With no decimal point, skip right side zeroes.
• 38 2 digits, 2 significant figures
• 5.06 3 digits, 3 significant figures
• 0.0041 5 digits, 2 significant figures
• 7,000. 4 digits, 4 significant figures
• 2,000 4 digits, 1 significant figure
Using Significant Figures
Add or Subtract Multiply or Divide
Keep the significant figures Keep the same number of
to decimal place of the least significant figures as the
accurate value, rounding as value with the fewest,
needed. rounding as needed.
• 4.361 + 14.2 = 18.6 • 4.361 14.2 = 61.9
• 12000 + 364 = 12000 • 12000 364 = 4.4 106
Absolute Uncertainty
Measure 50.0 cm.
There are three significant figures.
The smallest figure suggests an
accuracy of 0.1 cm.
This is also equal to 1 mm.
The absolute uncertainty has the same type of units
as the measurement.
Percent Uncertainty
Measure 50.0 cm.
Compare 0.1 cm to 50.0 cm.
The ratio is 0.1/50.0 = 0.002.
Multiply by 100 % to get 0.2 %.
The percent uncertainty has no units, and is either a
pure number or a percent.
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