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Unit 2: Units and Measurements
Vocabulary 1
British system
Metric system
SI system
kelvin
derived units
natural units
base unit
second
meter
kilogram
liter
density
Units d'Unités, or the
• Le Système International
International System of Units--more
commonly known as the SI system is an
internationally agreed upon system of
____________.
All measurements consist of two parts: a scalar
(__________) quantity and the unit designation.
In the measurement 8.5 m, the scalar quantity is
8.5 and the ____designation is meters.
A number indication “how much” and a unit
indicates “of what”.
• A base unit is a defined unit in a system of
measurement that is based on an object or
event in the physical world, and is
______________ of other units.
Nine fundamental units make up the SI system:
Temperature
Length
Time
Mass
Amount of a substance
Electric current
Light intensity
plane angles
solid angles
(K) kelvin
(m) meter
(s) second
(kg) kilogram
(mol) mole
(A) amphere
(cd) candela
(rad) radian
(sr) steradian
T-Scale
10-6
106
M
103
102
101
k
h da m
10-1
g
L
s
10-2
10-3
d c m
µ
Prefix Abbreviation Multiplicative Amount * The letter μ is the Greek lette
equivalent to an m and is called “mu” (pronounced “myoo”).
Prefix
giga
mega
Symbol
G
M
Factor
Sci Notation
1,000,000,000
1,000,000
Example
10E9
10E6
megagram
kilo
k
1,000
deci
d
1/10
centi
c
1/100
10E-2
milli
m
1/1000
10E-3
micro
µ
gigameter
1/1000000
10E3
10E-1
10E-6
nano
n
1/1000000000
pico
p
1/1000000000000
microgram
10E-9
10E-12
picometer (pm)
32˚Fahrenheit
0˚C
273.15 Kelvin
• The SI base unit of time is the _______ (s),
based on the frequency of radiation given
off by a cesium-133 atom.
• The SI base unit for ______is the meter (m),
the distance light travels in a vacuum in
1/299,792,458th of a second.
The meter is a little longer than a yard.
• The SI base unit of mass is the kilogram (kg),
about __________.
• The SI base unit of temperature
is the ______(K).
• Zero kelvin is the point where
there is virtually no particle
motion or kinetic energy, also
known as __________.
• Two other temperature scales
are Celsius and Fahrenheit.
• Many physical phenomena are measured in
units that are derived from SI units.
• A unit that is defined by a combination of base
units is called a ________.
• ________ is measured in cubic meters (m3),
but this is very large. A more convenient
measure is the liter, or one cubic decimeter
(dm3).
• Density is a derived unit, ______, the
amount of mass per unit volume.
• Density is a measure of how much matter
packed into a certain space.
• The density equation is _____________.
Vocabulary 2
significant figures
scientific notation
powers of ten
rounding numbers
dimensional analysis
conversion factor
Significant Figures
• Often, precision is limited by the tools
available.
• Significant figures include all known digits
plus one _____________ .
Rules for Significant Figures
–Rule 1: Nonzero numbers are always significant.
–Rule 2: Zeros between nonzero numbers are always
significant.
–Rule 3: All final zeros to the right of the decimal are
significant.
–Rule 4: Placeholder zeros are not significant. To
remove placeholder zeros, rewrite the number in
scientific notation.
–Rule 5: Counting numbers and defined constants have
an ________ number of significant figures.
The Atlantic-Pacific Rule:
"If a decimal point is Present, ignore zeros on the Pacific
(left) side. If the decimal point is Absent, ignore zeros on
the Atlantic (right) side. Everything else is significant."
If you're not in the Americas, you may prefer the following
less colorful way to say the same thing:
1.
Ignore leading zeros.
2.
Ignore trailing zeros, unless they come after a
decimal point.
3.
Everything else is significant.
Example Question: How many significant
figures are in the following numbers?
a. 0.000010 L
b. 907.0 km
c. 2.4050 x 10E-4 kg
d. 300,100,000 g
Hint: If a decimal point is included, count the
zeros. If there is no decimal point, the zeros do
not count. Do not start counting until the first
nonzero digit is reached as viewed from left to
right.
• Scientific notation can be used to express
any number as a number between 1 and 10
(the ________) multiplied by 10 raised to a
power (the ________).
• Count the number of places the decimal point
must be moved to give a coefficient between 1
and 10.
• The number of places moved equals the
value of the exponent.
• The exponent is _______ when the decimal
moves to the left and negative when the
decimal moves to the right.
800 = 8.0  10__
0.0000343 = 3.43  ____
• How many sig figs are in the numbers listed
above?
Addition and subtraction Involving measured
Values
–Exponents must be ____ ______.
–Rewrite values with the same exponent.
–Add or subtract coefficients.
Example Questions (answers in scientific notation):
a. 5.10 x 1020 + 4.11 x 1021b. 6.20 x 108 - 3.0 x 106c.
2.303 x 105 - 2.30 x 103d. 1.20 x 10-4 + 4.7 x 10-5e.
6.20 x 10-6 + 5.30 x 10-5f. 8.200 x 102 - 2.0 x 10-1
Multiplication and division
– To multiply, multiply the coefficients, then
_____ the exponents.
– To divide, divide the coefficients, then
_________ the exponent of the divisor from
the exponent of the dividend.
Example Problems:
a. (3 x 107 km) x (3 x 107 km)
b. (2 x 10-4 mm) x (2 x 10-4 mm)
c. (90 x 1014 kg) ÷ (9 x 1012 L)
d. (12 x 10-4 m ) ÷ (3 x 10-4 s)
Rounding Numbers
•________ are not aware of significant figures.
•Answers should not have more significant
figures than the original data with the fewest
figures, and should be rounded.
Rules for rounding
– Rule 1: If the digit to the right of the last significant
figure is less than 5, do not change the last
significant figure.
– Rule 2: If the digit to the right of the last significant
figure is greater than 5, round up to the last
significant figure.
– Rule 3: If the digits to the right of the last significant
figure are a 5 followed by a nonzero digit, round up
to the last significant figure.
– Rule 4: If the digits to the right of the last significant
figure are a 5 followed by a 0 or no other number at
all, look at the last significant figure. If it is odd, round
it up; if it is even, do not round up.
Round each number to five
significant figures. Write your
answers in scientific notation.
a. 0.000249950
b. 907.0759
c. 24,501,759
d. 300,100,500
• Addition and subtraction
– Round numbers so all numbers have the same
number of digits to the _______________.
• Multiplication and division
– Round the answer to the same number of significant
figures as the original measurement with the
________ significant figures.
Example Questions:
Complete the following calculations.
Round off your answers as needed.
a. 52.6 g + 309.1 g + 77.214 g
b. 927.37 mL - 231.458 mL
c. 245.01 km x 2.1 km
d. 529.31 m ÷ 0.9000 s
• Dimensional analysis is a systematic
approach to problem solving that uses
conversion factors to move, or convert, from
one unit to another.
• A ____________ is a ratio of equivalent
values having different units.
• A conversion factor is always equal to 1.
Multiplying a quantity by a conversion factor
does not change its value-because it is the
same as multiplying by 1-but the units of the
quantity can change.
Writing conversion factors
–_____________ are derived from equality
relationships, such as 1 dozen eggs = 12 eggs.
–Percentages can also be used as conversion
factors. They relate the number of parts of one
component to 100 total parts.
–A conversion factor must ________ one unit and
introduce a new one.
Vocabulary 3
accuracy
precision
error
percent error
graphs
x
x
• _____________ refers to how close a
measured value is to an accepted value.
• _____________ refers to how close a
series of measurements are to one another.
xx
xx
x
Both Good Precision
and Good Accuracy
x
x
x
x
x
Poor Precision
but Good Accuracy
x
xx
xx
x
Good Precision
Poor Accuracy
• _______ is defined as the difference
between and experimental value and an
accepted value.
• a- most precise
• b- most accurate
• The ________equation is:
error = experimental value – accepted value.
• Percent error expresses error as a percentage
of the accepted value.
• When you calculate percent error, ignore any
plus or minus signs because only the size of the
error counts.
• A graph is a _____ display of data that
makes trends easier to see than in a table.
• A circle graph, or pie chart, has wedges that
visually represent ________ of a fixed
whole.
• Bar graphs are often used to show how a
quantity varies across categories.
• On line graphs, independent variables are
plotted on the x-axis and dependent
variables are plotted on the _______.
• If a line through the points is straight, the
relationship is linear and can be analyzed
further by examining the _________.
• Interpolation is reading and estimating
values falling between points on the graph.
• Extrapolation is estimating values outside the
points by _________________.
This graph shows important ________
measurements and helps the viewer visualize a
trend from two different time periods.