1. Unit Systems
Conversions
Powers of 10
Physical Quantities
Dimensions
Dimensional Analysis
Scientific Notation
Computer Notation
Calculator Notation
Significant Figures
Math Using Significant Figures
Order of Magnitude
Estimation
Fermi Problems

2. What is a physical quantity?
A physical quantity is any quantity that can be measured with a certain mathematical precision.
Example: Force
What is a dimension?
The product or quotient of fundamental physical quantities, raised to the appropriate powers, to form a derived physical quantity.
Example: mass x length / time2 (ML/T2)
What is a unit?
A precisely defined (standard) value of physical quantity against which any measurements of that quantity can be compared.
Example: Newton = kilogram x meters / second2

3. Sytème International length temperature Kelvin (K) current meters (m)
time
seconds (s)
mass
kilograms (kg)
temperature
Kelvin (K)
current
Amperes (A)
amount of substance
Mole (mol)
luminous intensity
candela (cd)

4. US Customary System length temperature Fahrenheit (F) current
inches (in, ")
time
seconds (s)
mass
pounds (lb)
temperature
Fahrenheit (F)
current
Amperes (A)
amount of substance
Mole (mol)
luminous intensity
candela (cd)

5. Other units length Feet (ft, '), mile (m, mi), furlong, hand time
minute (m, min), hour (hr), second (s), fortnight, while
force
Newton (N)
temperature
Celsius (C)
energy
Joule (J)
power
Watt (W)
pressure
Pascal (P)
magnetic field
Tesla (T), Gauss (G)

6. Common conversion factors
length
1 in = 2.54 cm
time
60 s = 1 min, 60 min = 1 hr, 24 hours = 1 day, days= 1 yr
force
1 N = lb
energy
1 J = 107 erg, 1 eV = 1.602x10-19 J
power
1 hp = 746 W
pressure
1 atm = kPa
magnetic field
1 T = 104 G

7. How to convert units

8. Most commonly used prefixes for powers of 10
tera T 1,000,000,000,
giga G 1,000,000,
mega M 1,000,
kilo k
centi c
milli m
micro μ
nano n

9. Common physical quantities
Mass
Distance
Time
Speed / Velocity
Acceleration
Force

10. Dimensions of common physical quantities
Mass M
Distance L
Time T
Speed / Velocity L / T
Acceleration L / T2
Force M L / T2

11. What is the equation that relates force and mass?
Force M L / T2
Force = M (L / T2)
= M (L/T)2 / L
= M (L / T2) + M (L/T)2 / L
Possible Equations…
So how did Isaac Newton know which is correct?

12. What is scientific notation?
1,562,  x106
 x10-3

13. Using scientific notation in formulas
Addition and Subtraction
set both numbers to the same exponent
add or subtract the decimal numbers
the exponent of the sum is the same as that of the numbers being added
Multiplication
multiply the decimal numbers
add the exponents
Division
divide the decimal numbers
subtract the exponents

14. How do computer’s write scientific notation?

15. Using scientific notation in calculators
When putting numbers in a calculator, it is best to covert them to non-prefixed units first (e.g. 1mm  1x10-3 m) and then convert back to the desired units when the problem is complete.
When using a calculator, it is also better to put in the full number (e.g. 1350x10-3 m instead of 1.35 m for 1350 mm). In this way you will avoid many of the “decimal place errors” so common in this class.

16. Significant figures defined
Significant figures in a number indicate the certainty to which a number is known.
(For example 1350 mm is known to within ~0.5 mm.)
Other than leading zeros, all digits in a number are significant.
(For example has 10 significant figures.)
Numbers are rounded up or down to the nearest significant figure.

17. Significant figures are used because any further digits added to your number have no physical meaning.
Any physically measured number (including physical constants) will be written with the correct number of significant figures unless otherwise noted.
Numerical constants, such as the 4 or the π in the equation
have an infinite number of significant figures because they are NOT measured.

18. Using significant figures
When multiplying or dividing numbers, the calculated number has the same number of significant figures as the number with the least significant figures used in the calculation.

19. Using significant figures
When adding or subtracting numbers, the number of significant figures in the calculated number must be such that the decimal place of the result is not beyond the least decimal number in the numbers used in the calculation.

20. Examples using significant figures

21. Why do we use order of magnitude?
Order of magnitude is used to make estimates.
For example: How many professors are there in the U.S.?
(These kinds of questions are named for Enrico Fermi, who first proposed them.)
Order of magnitude is also used to check calculations.

22. Order of magnitude defined
To determine the order of magnitude of a number, you must put the number in scientific notation using one digit before the decimal.
(e.g  1.345x103
 x10-3)
If the decimal number is less than five, the order of magnitude is then the exponent. If it is greater than or equal to five, the order of magnitude is the exponent plus one.
1345 has order of magnitude 3
has order of magnitude -2

23. Estimation
Estimation is not the same as calculation. However, it will almost always be within one exponent of the calculated answer.
An estimate is a fast way to check a number or choose between two numbers given as an answer
Actual
Estimate

24. An Example Fermi Problem
To within an order of magnitude how many bars of soap are
sold in the United States each year?
There are about 1x108 people in the U.S. (the actual number is closer to 3x108).
Each person lives in a family of about 1 person (the average is really closer to 3).
Each family uses about 1 bar of soap each week (a better number would be 0.5).
There are about 100 weeks in a year (the number is actually 52).
Compare this to the actual answer

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