PSSA PREP:
• Compared to the charge and mass of a proton,
an electron has:
A. the same charge and a smaller mass
B. the same charge and the same mass
C. an opposite charge and a smaller mass
D. an opposite charge and the same mass
UNITS AND
CONVERSIONS
What will be covered:
• SI Units
• Metric Prefixes and Order of Magnitude
• Factor-label conversions
• Multi-dimensional conversions
How will it be tested:
The contents of this section will be embedded in EVERYTHING we do this
year. I will always take off points for incorrect or lack of units and poor
conversions. It is very important that we get these skills down right away, as
they will erode our grades if we don’t.
SI Units
• International System of Units
• SI (French: Le Système international d'unités)
• The modern form of the metric system.
• SI is NOT a static set of units
• The United States and the United Kingdom are pretty
much the only two countries that do not wholly and
singly acknowledge this system.
SI Units : Length
• The Meter (m)
• Historically, the metre was defined by the French
Academy of Sciences as the length between two marks
on a platinum-iridium bar, which was designed to
represent 1/10,000,000 of the distance from the equator
to the north pole through Paris.
• Today, it is defined by the International Bureau of
Weights and Measures as the distance travelled by light
in absolute vacuum in 1/299,792,458 of a second.
SI Units:Mass
• The Kilogram (kg)
• It is defined as being equal to the mass of the
International Prototype Kilogram.
• It is the only SI base unit with an SI prefix as part of its
name.
• It is also the only SI unit that is still defined in relation to
an artifact rather than to a fundamental physical
property that can be reproduced in different
laboratories.
• The mass of the kilogram is almost exactly equal to that
of one liter of water.
SI Units: Time
• The Second (s)
• The second is currently defined as the duration of
9,192,631,770 periods of the radiation corresponding to
the transition between the two hyperfine levels of the
ground state of the caesium-133 atom at absolute zero.
SI Units: Temperature
•
The Kelvin (K)
•
The definition of the kelvin has three parts:
• It fixes the magnitude of the kelvin unit as being
precisely 1 part in 273.16 parts the difference
between absolute zero and the triple point of
water;
• It establishes that one kelvin has precisely the
same magnitude as a one-degree increment on
the Celsius scale; and
• It establishes the difference between the two
scales’ null points as being precisely 273.15
kelvins (0 K = −273.15 °C and 273.16 K =
0.01 °C).
SI Units: Others
• SI units also exist for:
• electric current
• the amount of a substance
• luminous intensity
***These units will be introduced as we
encounter the topics throughout this
course.
PSSA Prep:
• Two streams begin at the same elevation and have equal
volumes. Which statement best explains why one stream
could be flowing faster than the other stream?
A. The faster stream contains more dissolved minerals.
B. The faster stream has a much steeper gradient.
C. The streams are flowing in different directions.
D. The faster stream has a temperature of 10°C, and
the slower stream has a temperature of 20°C.
Scientific Notation
• In scientific notation, all numbers are written in the form:
A x 10B C
-Where A is a real number between 1 and 10
-Where B is an integer
- Where C is the unit of measurement
Scientific Notation
A x 10B
-The notation x 10B can be interpreted as
“multiply A by ten B times”
Example:
3.5 x 104 m = 3.5 x 10 x 10 x 10 x 10 m = 35,000 m
-When B is negative, it should be interpreted as
“multiply A by one-tenth B times”
Example:
1 1 1
2.8 10 3 K  2.8 


10 10 10
 .0028K
Scientific Notation
Practice:
Put these numbers into scientific notation:
49,000 m
.00598 Kg
36,000,000 s
Significant Digits
-Significant Digits are the digits in a measurement that are
reliable.
Identifying Significant Digits:
1. Nonzero digits are always significant.
2. All final zeros after the decimal point are significant.
3. Zeros between two other significant digits are always
significant.
4. Zeros used solely as placeholders are not significant.
Significant Digits
How many significant digits does each number have?
A.) 15.45 m
The Rules:
B.) 306.29 kg
1. Nonzero digits are always
significant.
C.) 0.00436 L
D.) 34.07900 J
E.) 8.51 x 106 m
2. All final zeros after the decimal
point are significant.
3. Zeros between two other
significant digits are always
significant.
4. Zeros used solely as placeholders
are not significant.
Significant Digits
-These digits affect whether or not certain
calculations make sense to perform.
Example:
A man is measuring a hallway in which he plans to
install carpet. He measures the hallway and
records it to be 12 m long.
When his wife gets home, she asks if he
remembered that the carpet must go under the
baseboards. He truthfully states that he didn’t.
Should he add the extra 0.08 meters to his
measurement? Why or why not?
Significant Digits
Addition and Subtraction:
Find the least precise measurement, perform the
operation, and round the answer to the same place as the
least precise significant figure.
Example: Add 6.789 m + 43.5 m + 18 m
6.789 m
43.9 m
+18.
m
68.689 m = 69 m
Significant Digits
Multiplication and Division:
Perform the operation, then count the significant figures of
the factor with the fewest sig. figs. Round your final
answer so that it has the same number of sig. figs.
Example: Divide: 205 m / .347 s / 5 s
3 sig. fig.
3 sig. fig.
1 sig. fig.
 205m 


 .347s   118.15 m
2
5s
s
m

= 100
?
2
s
SI Prefixes
• http://en.wikipedia.org/wiki/SI_prefix
The metric prefix is used to allow measurements to
become decimal-multiples that fall between .1 and 1000.
SI Prefixes
• The SI prefix takes the place of the order of magnitude
multiple when a measurement is written in scientific
notation:
• 8,000,000 m = 8.0 x106 m = 8.0 Mm
Orders of Magnitude
• A way of comparing relative changes in
measurements.
• When something is about 10x bigger than
another, we say that it is one “order of magnitude”
larger than the other.
• A scientist leaves 30 bacteria in a dish over night.
When he returns 12 hours later, he sees that there are
now 400. He accurately states that in 12 hours, the
bacteria has increased it’s population by an order of
magnitude.
Orders of Magnitude
Simpsons Power of Ten movie from
Introduction Media Files
Order of magnitude
• Orders of Magnitude can be used to make vague
estimates for numbers that would be very difficult
to find. . . These estimates are often called “Fermi
Estimations”
• When checking one’s solution to a problem, or
wondering whether or not a measurement was
taken correctly, it is wise to check if the answer is
on the correct order of magnitude
Orders of Magnitude
~ 1 byte (1 note of a song)
Orders of Magnitude
~ 800 Hectobytes
(A Nintendo song)
Orders of Magnitude
~ 1400 kilobytes
(one low quality mp3)
Orders of Magnitude
~100 Megabytes
(One Medium Quality .mp3 Album
or 1 High quality .wav file)
Orders of Magnitude
~1 gigabyte
(10 .mp3 albums or
1 high quality .wav album)
Orders of Magnitude
~1 terabyte
(100,000 high quality .mp3 songs, or
1 music store of high quality .wav files)
Resources
• http://en.wikipedia.org/wiki/siunits
• Time Service Department, United States Naval
Observatory