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Honors Chemistry
Chapter 2 Analyzing Data
Notes Outline
2.1 Units and Measurement
Main Idea: Chemists use an internationally recognized system of units to communicate
their findings.
1960 Le Systeme Internationale d’Unites
The United States and Liberia are the only nations that use the English system of
measurement. All other nations use the SI system.
base unit – a defined unit in a system of measurement that is based on an object or event
in the physical world and is independent of other units
SI Base Units
Quantity
Time
Length
Mass
Temperature
Amount of a substance
Electric current
Luminous intensity
Base Unit(Symbol)
second (s)
meter (m)
kilogram (kg)
Kelvin (K)
mole (mol)
ampere (A)
candela (cd)
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Metric Prefixes
Exa
Peta
Tera
Giga
Mega
Kilo
Hecto
Deca
Base
deci
centi
milli
micro
nano
pico
femto
atto
E
P
T
G
M
K
H
D
d
c
m
µ
n
p
f
a
1018
1015
1012
109
106
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
Temperature
temperature – quantitative measurement of the average kinetic energy of the particles
that make up an object
Scale
Fahrenheit
Celsius
Kelvin
˚F = 9/5(˚C) + 32
Freezing Point of Water
32˚F
0˚C
273 K
˚C = 5/9(˚F – 32)
Boiling Point of Water
212˚F
100˚C
373 K
K = ˚C + 273
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derived unit – combination of base units
volume – space occupied by an object
Finding the Volume of a Solid

Volume of a Regular Solid = length x width x height

Volume of an Irregular Solid = water displacement
Volume = (volume of water + solid) – (original volume of water)
Helpful Volume Conversions
1 L = 1 dm3 = 1000 cm3
1 mL = 1 cm3
1 L = 1000 mL
Density
density – amount of mass per unit of volume
D=m
V
Density = mass/volume
Example Problem 2.1 (page 38) When a piece of aluminum is placed in a 25-mL graduated
cylinder that contains 10.5 mL water, the water level rises to 13.5 mL. What is the mass of
the aluminum?
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Practice Problems #1-3 (page 38)
1. Is a cube that has a mass of 20 g and a volume of 5 cm3 made of aluminum? Explain
your answer.
2. What is the volume of a sample that has a mass of 20 g and a density of 4 g/mL?
3. A 147-g piece of metal has a density of 7.00 g/mL. A 50-mL graduated cylinder
contains 20.0 mL of water. What is the final volume after the metal is added to the
graduated cylinder?
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2.2 Scientific Notation and Dimensional Analysis
Main Idea: Scientists often express numbers in scientific notation and solve problems
using dimensional analysis.
scientific notation – expresses any number as a number between 1 and 10 (known as a
coefficient) multiplied by 10 raised to a power (known as an exponent)
Example Problem 2.2 Write the following data in scientific notation:
a) The diameter of the sun is 1 392 000 km.
b) The density of the sun’s lower atmosphere is 0.000 000 028 g/cm3.
Practice Problems (page 41)
11) Express each number in scientific notation.
a) 700
b) 38 000
c) 4 500 000
d) 685 000 000 000
e) 0.005 4
f) 0.000 006 87
g) 0.000 000 076
h) 0.000 000 000 8
12) Express each quantity in regular (standard) notation along with its appropriate unit.
a) 3.60 x 105 s
b) 5.4 x 10-5 g/cm3
c) 5.060 x 103 km
d) 8.9 x 1010 Hz
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Addition and Subtraction
 Exponents must be the same
 Add or subtract the coefficients
 Exponent stays the same
Practice Problems (page 42)
13) Add or subtract as indicated.
a) (5 x 10-5) + (2 x 10-5)
b) (7 x 108) – (4 x 108)
c) (9 x 102) – (7 x 102)
d) (4 x 10-12) + (1 x 10-12)
14) Add or subtract as indicated. Remember that exponents must be the same!
a) (1.26 x 104kg) + (2.5 x 103 kg)
b) (7.06 x 10-3 kg ) + (1.2 x 10-4 kg)
c) (4.39 x 105 kg) – (2.8 x 104 kg)
d) (5.36 x 10-1 kg) – (7.40 x 10-2 kg)
Multiplication and Division
Exponents do not need to be the same
Multiplication – multiply coefficients and ADD exponents
Division – divide coefficients and SUBTRACT exponents
Example Problem 2.3
a) (2 x 103) x (3 x 102)
b) (9 x 108) ÷ (3 x 10-4)
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Practice Problems (page 43)
15) Multiply or divide as indicated.
a) (4 x 102) x (1 x 108)
b) (2 x 10-4) x (3 x 102)
c) (6 x 102) ÷ (2 x 101)
d) (8 x 104) ÷ (4 x 101)
16) Calculate
a) the area of a rectangle with sides measuring 3 x 101 cm and 3 x 10-2 cm
b) the area of a rectangle with sides measuring 1 x 103 cm and 5 x 10-1 cm
c) the density of a substance having a mass of 9 x 105 g and a volume of 3 x 10-1 cm3
d) the density of a substance having a mass of 4 x 10-3 g and a volume of 2 x 10-2 cm3
Dimensional Analysis
dimensional analysis – systematic approach to problem solving
that uses conversion factors to move, or convert, from one
unit to another
conversion factor – ratio of equivalent values having
different units
Practice Problems (page 45)
17) Write two conversion factors for each of the following:
a) a 16% (by mass) salt solution
b) a density of 1.25 g/mL
c) a speed of 25 m/s
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18) What conversion factors are needed to convert:
a) nanometers to meters?
b) density given in g/cm3 to a value in kg/m3?
19) Use metric prefixes to solve the following:
a) convert 360 s to ms
b) convert 4800 g to kg
c) convert 5600 dm to m
d) convert 72 g to mg
e) convert 2.45 x 102 ms to s
f) convert 5 µm to m
g) convert 6.800 x 103 cm to km
h) convert 2.5 x 101 kg to Mg
20) Write the conversion factors needed to determine the number of seconds in one year.
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Example Problem 2.4 In ancient Egypt, small distances were measured in Egyptian cubits.
An Egyptian cubit was equal to 7 palms, and 1 palm was equal to 4 fingers. If 1 finger was
equal to 18.75 mm, convert 6 Egyptian cubits to meters.
Practice Problems (page 46)
21) A speedometer reads 65 miles per hour. What is the car’s speed in km/h? (1 km = 0.62
miles)
22) How many seconds are in 24 h?
23) Vinegar is 5% acetic acid by mass and has a density of 1.02 g/mL. What mass of acetic
acid, in grams, is present in 185 mL of vinegar?
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2.3 Uncertainty in Data
GPS: SCSh3e, 5b-e, 9a, c-d
Main Idea: Measurements contain uncertainties that affect how a calculated result is
presented.
accuracy – how close a measured value is to an accepted value
precision – how close a series of measurements are to one another
Accurate, Not Precise
Precise, Not Accurate
Accurate and Precise
Not Accurate or Precise
error – the difference between an experimental value and an accepted value
error = experimental value – accepted value
percent error – expresses error as a percentage of the accepted value
percent error =
| error | x 100
accepted
value
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Example Problem 2.5 Use the following data to calculate student A’s percent error in each
trial. Report answers to two places after the decimal point. (accepted = 1.59 g/cm3)
Trial 1
Trial 2
Trial 3
Average
Student A
Density
Error
1.54 g/cm3
-0.05
3
1.60 g/cm
+0.01
3
1.57 g/cm
-0.02
3
1.57 g/cm
Student B
Density
Error
1.40 g/cm3
-0.19
3
1.68 g/cm
+0.09
3
1.45 g/cm
-0.14
3
1.51 g/cm
Student C
Density
Error
1.70 g/cm3
+0.11
3
1.69 g/cm
+0.10
3
1.71 g/cm
+0.12
3
1.70 g/cm
Practice Problems (page 49)
Use the data in the table above to answer the following questions.
32) Calculate the percent errors for Student B’s trials.
33) Calculate the percent errors for Student C’s trials.
34) Based on percent error, which student’s trial was the most accurate? least accurate?
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Significant Figures
significant figures – all known digits plus one estimated digit
Rules for Recognizing Significant Figures
1) Nonzero digits are always significant.
2) Zeros between nonzero digits are always significant. (captive or sandwiched zeros)
3) All final zeros to the right of the decimal point are significant. (trailing zeros)
4) Place holder zeros are not significant.
5) Counting numbers and defined constants have an infinite number of significant
figures.
Example Problem 2.6 Determine the number of significant figures in the following masses:
a) 0.000 402 30 g
b) 405 000 kg
Practice Problems (page 51)
35) a) 508.0 L
b) 820 400.0 L
c) 1.0200 x 105 kg
d) 807 000 kg
36) a) 0.049 450 s
b) 0.000 482 mL
c) 3.1587 x 10-4 g
d) 0.008 4 mL
37) Write the numbers 10, 100, and 1000 in scientific notation with two, three, and four
significant figures, respectively.
Rules for Rounding
1) If the digit to the right of the last significant figure is less than 5, do not change
the last significant figure.
2) If the digit to the right of the last significant figure is greater than or equal to 5,
round up the last significant figure.
Practice Problems (page 53)
38) Round each number to four significant figures.
a) 84 791 kg
b) 38.5432 g
c) 256.75 cm
d) 4.9356 m
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39) Round each number to four significant figures, and write the answer in scientific
notation.
a) 0.000 548 18 g
b) 136 758 kg
c) 308 659 000 mm
d) 2.014 5 mL
Addition and Subtraction
When adding and subtracting, the answer must have the same number of digits to the
right of the decimal as the original value having the fewest number of digits to the right
of the decimal point.
Example Problem 2.7 A student measured the length of his partner’s shoes. If the lengths
are 28.0 cm, 23.538 cm, and 25.68 cm, what is the total length of the shoes?
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