1. Measurement
Why are precise measurements and calculations essential to a study of physics?

2. Measurement & Precision
The precision of a measurement depends on the instrument used to measure it.
For example, how long is this block?

3. Measurement & Precision
Imagine you have a piece of string that is exactly 1 foot long.
Now imagine you were to use that string to measure the length of your pencil. How precise could you be about the length of the pencil?
Since the pencil is less than 1 foot, we must be dealing with a fraction of a foot. But what fraction can we reliably estimate as the length of the pencil?

4. Measurement & Precision
Suppose the pencil is slightly over half the 1 foot string. You guess, “Well it must be about 7 inches, so I’ll say 7/12 of a foot.”
Here’s the problem: If you convert 7/12 to a decimal, you get
Can you reliably say, without a doubt, that the pencil is and not or 0.582?
You can’t. The string didn’t allow you to distinguish between those lengths… you didn’t have enough precision.
So, what can you estimate, reliably?

5. Measurement & Precision
Basically, you have one degree of freedom… one decimal place of freedom.
So, the only fractions you can use are tenths!
You can only reliably estimate that the pencil is 0.6 ft long. It’s definitely more than 0.5 ft long and definitely less than 0.7 ft long.
Thus, precision determines the number of significant figures we use to report measurements.
In order to increase the precision of their measurements, physicists develop more-advanced instruments.

6. How big is the beetle? Measure between the head and the tail!
Between 1.5 and 1.6 in
Measured length: 1.54 in
The 1 and 5 are known with certainty
The last digit (4) is estimated between the two nearest fine division marks.
Copyright © by Fred Senese

7. How big is the penny? Measure the diameter.
Between 1.9 and 2.0 cm Estimate the last digit.
What diameter do you measure?
How does that compare to your classmates?
Is any measurement EXACT?
Copyright © by Fred Senese

8. What Length is Indicated by the Arrow?

9. Significant Figures Indicate precision of a measured value
1100 vs
Which is more precise? How can you tell?
How precise is each number?
Determining significant figures can be tricky.
There are some very basic rules you need to know. Most importantly, you need to practice!

10. Counting Significant Figures
The Digits
Digits That Count
Example
# of Sig Figs
Non-zero digits
ALL
         4.337 4
Leading zeros
(zeros at the BEGINNING)
NONE
         2
Captive zeros
(zeros BETWEEN non-zero digits)
         7
Trailing zeros
(zeros at the END)
ONLY IF they follow a
significant figure AND
there is a decimal
point in the number
but 8900
Leading, Captive AND Trailing Zeros
Combine the
rules above
but 3020 3
Scientific Notation
        7.78 x 103

11. Calculating With Sig Figs
Type of Problem
Example
MULTIPLICATION OR DIVISION:
Find the number that has the fewest sig figs. That's how many sig figs should be in your answer.
3.35 x mL = mL rounded to 15.6 mL
3.35 has only 3 significant figures, so that's how many should be in the answer.  Round it off to 15.6 mL
ADDITION OR SUBTRACTION:
Find the number that has the fewest digits to the right of the decimal point. The answer must contain no more digits to the RIGHT of the decimal point than the number in the problem.
64.25 cm cm = cm rounded to cm
64.25 has only two digits to the right of the decimal, so that's how many should be to the right of the decimal in the answer. Drop the last digit so the answer is cm.

12. Scientific Notation Number expressed as: 5.63 x 104, meaning
Product of a number between 1 and 10 AND a power of 10
5.63 x 104, meaning
5.63 x 10 x 10 x 10 x 10
or 5.63 x 10,000
ALWAYS has only ONE nonzero digit to the left of the decimal point
ONLY significant numbers are used in the first number
First number can be positive or negative
Power of 10 can be positive or negative

13. When to Use Scientific Notation
Astronomically Large Numbers
mass of planets, distance between stars
Infinitesimally Small Numbers
size of atoms, protons, electrons
A number with “ambiguous” zeros
59,000
HOW PRECISE IS IT?

14. Exponent of Zero Means “1” 100 = 1
Powers of 10
Positive Exponents
Exponent of Zero Means “1” 100 = 1

15. Exponent of Zero Means “1” 100 = 1
Powers of 10
Negative Exponents
Exponent of Zero Means “1” 100 = 1

16. Converting From Standard to Scientific Notation
Move decimal until it is behind the first sig fig
Power of 10 is the # of spaces the decimal moved
Decimal moves to the left, the exponent is positive
Decimal moves to the right, the exponent is negative
 x (decimal moves 2 spots left)
 x (decimal moves 4 spots right)

17. Converting From Scientific to Standard Notation
Move decimal point
# of spaces the decimal moves is the power of 10
If exponent is positive, move decimal to the right
If exponent is negative, move decimal to the left
4.285 x 102  (move decimal 2 spots right)
4.285 x 10-4  (decimal moves 4 spots left)

18. Systems of Measurement
Why do we need a standardized system of measurement?
Scientific community is global.
An international “language” of measurement allows scientists to share, interpret, and compare experimental findings with other scientists, regardless of nationality or language barriers.
By the 1700s, every country used its own system of weights and measures. England had three different systems just within its own borders!

19. Metric System & SI
The first standardized system of measurement: the “Metric” system
Developed in France in 1791
Named based on French word for “measure”
based on the decimal (powers of 10)
Systeme International d'Unites (International System of Units)
Modernized version of the Metric System
Abbreviated by the letters SI.
Established in 1960, at the 11th General Conference on Weights and Measures.
Units, definitions, and symbols were revised and simplified.

20. Components of the SI System
In this course we will primarily use SI units.
The SI system of measurement has 3 parts:
base units
derived units
prefixes
Unit: measure of the quantity that is defined to be exactly 1
Prefix: modifier that allows us to express multiples or fractions of a base unit
As we progress through the course, we will introduce different base units and derived units.

21. SI: Base Units length meter m mass kilogram kg time second s
Physical Quantity
Unit 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

22. SI: Derived Units area square meter m2 volume cubic meter m3 speed
Physical Quantity
Unit Name
Symbol
area
square meter m2
volume
cubic meter m3
speed
meter per
second
m/s
acceleration
second squared
m/s2
weight, force
newton N
pressure
pascal Pa
energy, work
joule J

23. Prefixes Prefix Symbol Numerical Multiplier Exponential Multiplier
yotta Y
1,000,000,000,000,000,000,000,000
1024
zetta Z
1,000,000,000,000,000,000,000
1021
exa E
1,000,000,000,000,000,000
1018
peta P
1,000,000,000,000,000
1015
tera T
1,000,000,000,000
1012
giga G
1,000,000,000
109
mega M
1,000,000
106
kilo k
1,000
103
hecto h
100
102
deca da 10
101
no prefix means: 1

24. Prefixes Prefix Symbol Numerical Multiplier Exponential Multiplier
no prefix means: 1
100
deci d
0.1
10¯1
centi c
0.01
10¯2
milli m
0.001
10¯3
micro
10¯6
nano n
10¯9
pico p
10¯12
femto f
10¯15
atto a
10¯18
zepto z
10¯21
yocto y
10¯24

25. Unit Conversions “Staircase” Factor-Label Method Type Visual
Mathematical
What to do…
Move decimal point the same number of places as steps between unit prefixes
Multiply measurement by conversion factor, a fraction that relates the original unit and the desired unit
When to use…
Converting between different prefixes between kilo and milli
Converting between SI and non-SI units
Converting between different prefixes beyond kilo and milli

26. “Staircase” Method
Draw and label this staircase every time you need to use this method, or until you can do the conversions from memory

27. “Staircase” Method: Example
Problem: convert 6.5 kilometers to meters
Start out on the “kilo” step.
To get to the meter (basic unit) step, we need to move three steps to the right.
Move the decimal in 6.5 three steps to the right
Answer: 6500 m

28. “Staircase” Method: Example
Problem: convert cm to km
Start out on the “centi” step
To get to the “kilo” step, move five steps to the left
Move the decimal in five steps the left
Answer: km

29. Factor-Label Method
Multiply original measurement by conversion factor, a fraction that relates the original unit and the desired unit.
Conversion factor is always equal to 1.
Numerator and denominator should be equivalent measurements.
When measurement is multiplied by conversion factor, original units should cancel

30. Factor-Label Method: Example
Convert 6.5 km to m
First, we need to find a conversion factor that relates km and m.
We should know that 1 km and 1000 m are equivalent (there are 1000 m in 1 km)
We start with km, so km needs to cancel when we multiply. So, km needs to be in the denominator

31. Factor-Label Method: Example
Multiply original measurement by conversion factor and cancel units.

32. Factor-Label Method: Example
Convert 3.5 hours to seconds
If we don’t know how many seconds are in an hour, we’ll need more than one conversion factor in this problem