1. Numbers

2. 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: = 4.56 x 105
Negative powers for small numbers: = 7.53 x 10-3
Write a number in scientific notation with only one non-zero value to the left of the decimal place.

3. Order of Magnitude
You
Lecture Hall
Faraday West
NIU
5’9” = 1.75 m ≈ 100 m
14 m ≈ 101 m
80 m ≈ 102 m
2000 m ≈ 103 m
Each of these lengths is different by about one order of magnitude

4. Map Lengths
Huskie Stadium
DeKalb City
DeKalb County
Illinois
100 m ≈ 102 m
4 km = 4000 m ≈ 103 m
30 km = 30,000 m ≈ 104 m
400 km ≈ 105 m
Mapping software uses scaling factors, about two steps per order of magnitude

5. 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.

6. 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
digits, 3 significant figures
digits, 2 significant figures
7, digits, 4 significant figures
2,000 4 digits, 1 significant figure

7. Using Significant Figures
Add or Subtract
Keep the significant figures to decimal place of the least accurate value, rounding as needed.
= 18.6
= 12000
Multiply or Divide
Keep the same number of significant figures as the value with the fewest, rounding as needed.
4.361  14.2 = 61.9
12000  364 = 4.4  106

8. 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.

9. Percent Uncertainty
Measure 50.0 cm.
Compare 0.1 cm to 50.0 cm.
The ratio is 0.1/50.0 =
Multiply by 100 % to get 0.2 %.
The percent uncertainty has no units, and is either a pure number or a percent.