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

Scientific Notation Review
Dimensional Analysis:

Next Week:
◦ Challenge Problem Set 1
DUE on Monday, Feb. 2nd at
11 pm
 The English System of units vs. Metric
◦ Introductory Course Survey
System of units (SI)
DUE Wednesday, Feb 4th at
 Prefixes (kilo-, centi-, milli-, etc.)
11 pm
◦ A systematic method for
◦ Before coming to lecture:
performing unit conversions
 Formulating different conversion factors
 Read material for Lecture
 Common errors & misconceptions
3: Chapter 1: Sections 1.1◦ Working with Compound Units
1.5, pp. 26-38
◦ Numbers and Units:
 Example: Density calculations
Measurement in Chemistry
Qualitative measurements – Observations that describe
a substance, mixture, reaction, or other process in
WORDS.
Quantitative measurements – Observations that
describe a property with NUMBERS and UNITS.
In 1999, the Mars Climate Orbiter was
lost in the Martian atmosphere because
two separate engineering teams
reported their calculations WITHOUT
UNITS, & failed to communicate with
the units to each other.
The total cost of the mission
was $327.6 MILLION!
UNITS and Quantitative measurements

Numbers often make no sense if we do
not have some sort of reference or
standard to compare them to.

Nearly all numbers MUST be
followed by a unit label.

The unit indicates the standard against which the
number is measured.
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UNITS and Quantitative measurements

The metric system is a system of measurement based on
multiples of ten.

In the metric system, a prefix may be added to the base
unit to change the value of the unit by a factor of ten.
The base unit is a reference to the standard.

The English system of measurement is not based on
powers of ten, and is therefore more difficult to use in
calculations.

Scientists almost exclusively work in the metric or SI
system.
Base units: The Système Internationale (SI) base units
are defined from some physically observable and
reproducible quantity. The base units are:
Quantity
Unit
Length
meter
Symbol
Mass
kilogram (gram)
Time
second
S
Temperature
kelvin
K
Amount of a substance
mole
mol
Electric Current
ampere
A
Luminous Intensity
candela
cd
m
kg (g)
Metric Prefixes: The prefixes below modify any of the base metric units by
a power of 10. TO MEMORIZE: prefixes common to chemistry.
Prefix
Symbol
Multiple
Tera-
T
1012
1,000,000,000,000
Giga-
G
109
1,000,000,000
Mega-
M
106
1,000,000
kilo-
k
103
1,000
hecto-
h
102
100
deka-
dk
101
10
100
1
base unit
Multiple
deci-
d
101
0.1
centi-
c
102
0.01
milli-
m
103
0.001
micro-

106
0.000 001
nano-
n
109
0.000 000 001
pico-
p
1012
0.000 000 000 001
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Scientific Notation

A tool for expressing incredibly large or incredibly small
numbers WITHOUT using lots of zeros.
◦ Scientific notation is the combination of a
exponential of 10 (10x).
and an
Example:
There are approximately 400,000,000,000 stars in our galaxy.
x 1011
1011 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 =
100,000,000,000
In proper scientific notation: The decimal part of the
number is always expressed somewhere between 1 
n < 10.
Scientific Notation on the Calculator
To put an exponential number in your calculator, follow the
examples below:
To enter 7.35 x 105, press:
[7] [.] [3] [5]
[EE]
[5]
102, press:
To enter 4.5 x
[4] [.] [5]
Note:
[EE]
[+/-]
[2]
If your calculator does not have the [EE] key, use
the [EXP] key.
To read an exponential off of your calculator, follow these
examples:
4.153 04 would be read as 4.153 x 104 or 41,530
8.1 02 would be read as 8.1 x 102 or 0.081
Various calculator readouts of 8 x 103:

Important note: You must express numbers on paper with
proper scientific notation to receive full credit!
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Relationships of selected U.S. and Metric Units

In the U.S., many of the everyday measurements we use are
based on the older English system.

We primarily use the metric system for measurements in labs
in the U.S. However it is still often necessary to make some
conversions to the metric system. These conversion factors
will be given if necessary.
Length
1 in = 2.54 cm
Mass
1 lb = 0.4536 kg
Volume
1 qt = 0.9464 L
1 yd = 0.9144 m
1 lb = 16 oz
4 qt = 1 gal
1 mi = 1.609 km
1 oz = 28.35 g
1 mi = 5280 ft
Metric Conversions

First think intuitively about the conversion:
$1 → ? cents
◦ Which unit is larger? Which unit is smaller?
◦ If converting a number from a larger unit to a smaller unit, the
number should become bigger.

Converting from a larger prefix to a smaller one:
◦ Move the decimal to the right:
0.896 m  mm
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Converting from a smaller prefix to a larger one:
◦ Move the decimal to the left:
750 mL  L
DIMENSIONAL ANALYSIS:
A method of solving chemical problems in which the
units are used to set up the solution to a problem.

Dimensional analysis uses a series of ratios (conversion factors) to
convert one unit into another unit.
24 inches
How many feet?
ANSWER
Starting Quantity
24 inches
1 foot
12 inches
= 2 feet
Conversion Factor
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Steps in dimensional analysis
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Identify the conversion to be performed:
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Setup a Dimensional Analysis table.
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Insert conversion factors to ELIMINATE UNWANTED
UNITS and introduce the desired units.

Compute. Be careful to include parentheses where
necessary.
GIVEN UNITS  DESIRED UNITS
Note that a dimensional analysis table is identical to
multiplying by fractions.
Dimensional Analysis Examples
1.5 fm
=________ pm
90 nm
=________ cm
Compound Units

Volume (space occupied by matter) can be considered a
compound unit. The simplest formula for volume is for the
volume of a box: Volume = (length)∙(width)∙(height)
◦ Consider a box with:
 length = 5.0 cm, width = 3.0 cm, height = 7.0 cm
 Volume = 5.0 cm x 3.0 cm x 7.0 cm = 105 cm3
Just as the numbers are multiplied, so are the units.

Velocity is another common compound unit. It combines
distance and time.
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Volume Conversion Factors
Common Problem
dm3  cm3
1 dm = 10 cm
(1 dm)3 = (10 cm)3
1 dm3 = 1000 cm3
Compound Unit Conversion
Convert: 4.7 L  __________ ft3
Given: 1 Liter = 1 dm3 & 1 m = 3.28 ft
Dimensional Analysis Examples
0.0233 ps
=________ s
9.65 x 108 cg
=________ kg
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Compound Unit Conversion
Convert: 3.0 x 108 m/s  __________ ft/ns
Compound Unit Conversion
Convert: 1.5 in/yr  ? nm/s
California uses approximately 82 million acre-feet
(MAF) of water per year. If this volume was
confined to the shape of a cube, what would be the
length of one side of the cube in miles?
Given: 1 acre-foot = 43,560 ft3
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Density

Density is a physical property of matter that describes the
relationship between mass and volume of a substance.
𝑀𝑎𝑠𝑠
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑉𝑜𝑙𝑢𝑚𝑒

Density is an intensive property of matter - A substance will have
a characteristic density that is independent of the amount of the
substance present.
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In lay terms, we might say it describes how "heavy" a substance is
(a misuse of the word).
Density Sample Calculation
What is the mass of a piece of iron with a volume of 35
cm3?
Given: the density of iron = 7.874 g/cm3
Problem Solving Examples
A neutron star has a density of about 100 million tons per
teaspoon (ton/tsp). What volume of a neutron star (in
cm3) would have the same mass as a Boeing 747, which
weighs 358,000 lbs.?
Given: 1 ton = 2000 lbs. & 1 tsp ≈ 4.92 cm3
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