1. Measurements In Physics
A. Units: 1. Physical Quantities - are anything that we can measure. - ex.( length, time, temp, mass, etc.) 2. Why are units important? - Numbers without units are meaningless - Not enough information without units

2. 3. Unit Systems - We use the SI system or metric system - There are 7 base (fundamental) units
Base Quantity
Name
Symbol
length
meter m
mass
kilogram kg
time
second s
electric current
ampere A
temperature
kelvin K
amount of substance
mole
mol
luminous intensity
candela cd

3. Measurements In Physics
- all other units can be derived (formed) from a combination of the 7 base units (similar to the alphabet) - Units are treated like algebraic quantities in EQUATIONS - ex: Volume = length3 = m3 Density = mass / volume = kg/ m3

4. Metric Conversions B. Metric Conversions
- Changing one unit of measurement to another
1. Dimensional Analysis
- The skill or process of converting units (factor labeling)

5. Method 1 Staying within the same base unit (metric system) Example:
grams – kilograms
liters – milliliters
meters - kilometers
Need:
Prefixes

6. 1 The Process Name Kilo Hecto Deka Base Unit (g), (m), (l) Deci Centi
Step 1:
Decide what column you are starting with (unit)
Step2:
Decide what column you want to finish with (unit)
Step3:
Count the number of columns from start to finish and MOVE the decimal point the same number and direction
Fill any open spots with ZEROS
Name
Kilo
Hecto
Deka
Base Unit
(g), (m), (l)
Deci
Centi
Milli
Abbreviation k h da d c m
Value 1
1000
100 10
1/10
1/100
1/1000
Examples:

7. Method 2 Converting between 2 different systems of measurements
(metric system to english system)
Within the metric system (method 1)
Example:
meters (m) – inches (in.)
feet (ft) – inches (in)
kilograms (kg) – pounds (Lbs)
Need:
Conversion Factor
1 ft = 12 inches

8. Process
Step 1:
Identify the conversion factor between the units you have to start and the units you want to end with
Step 2:
set up a ratio (fraction) with your given numbers and your conversion factor
Place the unit you want on top and the unit to cancel out on the bottom

9. Examples:
67.89cg = ? Kg
89.35km = ? m
3 m = ? Inches (1m = 39.4inch)
150 lbs = ? Kg (1kg = 2.21lbs)
6 hrs = ? sec

10. Measurements In Physics
Prefixes
See table 1-4 page 10 of text

11. C. Scientific Notation 1. Numbers in science can be extremely small or large 2. The general form is: A x 10n A = any number from Usually an integer greater than 1 but less than 10 n = the number and direction to move the decimal point to get the original number (neg = move left) (pos = move right)

12. 2.99 X 108 m/s Ex. Speed of Light 299,792,458 m/s = Diameter of hair

13. 3. Adding and Subtracting - the “n” value must be the same for each number. (you may have to change one of the numbers so they match) - then just add/subtract the “A’s” and keep the “n” the same Ex. 3.2x x103 = 1.5x10-1 – 3x10-2 =
3.2x x104 = 3.69x104
1.5x10-1 – 0.3x10-1 = 1.8x10-1

14. 4. Multiplying - multiply the “A’s” as usual - add the “n” value for each number (remember how to add negative #’s) Ex. 4.32x103 x 2x108 =
8.64x1011

15. - Divide the “A’s” as usual
5. Dividing
- Divide the “A’s” as usual
- subtract the “n” values for each number (remember how to subtract negative #’s)
Ex.
4.32x103 / 2x108 =
2.16x10-5

16. Measurements In Physics
D. Accuracy and Precision
1. Accuracy – closeness of a measurement to the accepted value for a specific physical quantity.
Expresses as error
Absolute error
Ea = |O - A |
Ea = absolute error
O = observed (trial) value
A = accepted value

17. Measurements In Physics
Relative Error (percent error)
Er = ( Ea / A ) x 100%
Er = relative error

18. Measurements
2. Precision – how close your trials are to each other. (the repeatability of the process.)
Measured as deviation
Absolute deviation
Da = |O - m |
Da = absolute deviation
m = mean of your trials
Relative Deviation
Dr = ( Da / m) x 100%

19. Ex.
You do an experiment to confirm the acceleration of gravity id 9.8m/s2 on the surface of the earth. Your trials are 10.2m/s2 , 9.9m/s2 , and 10.1m/s2 .
What is your absolute error for trial 1?
What is the relative error for trial 1?
What is the absolute deviation for trial 1?
What is the relative deviation for trial 1?