Measuring Matter
How can we keep track of all of
this “stuff”?
Measuring Matter in Two Ways
Qualitative Measurements: which are
usually descriptive like observations.
Now it is important to start making…
Quantitative Measurements: are in the form
of numbers and units.
The Powers of Ten
 Picture a microscopic
cell.
 Picture the galaxy.
Scientific Notation
 Scientists need a way to express extremely
LARGE and extremely SMALL numbers in
their quantitative measurement.
 Scientific notation shows the product of two
numbers:
A coefficient X 10 to some exponent
Scientific Notation
Remember that a coefficient is simply a number
that you multiply an expression by.
**In scientific notation1≤ coefficient <10.
Also remember that 10 to some power is simply ten
multiplied by itself that many times.
Ex. 103 = 10 x 10 x 10
Also, ten to a minus power is dividing by ten that
many times.
Examples of the use of Scientific
Notation
 I like to run. For every one mile, I have run 1609
meters.
 Expressed in scientific notation, this is
1.609 x 103 meters
When you multiply something times ten THREE
times, you move the decimal place to the right
three times.
More examples
 The diameter of a human hair is 0.000 008
meters.
 Expressed in scientific notation that is,
8.0 x 10-6 meters
Note: The negative sign moves the decimal
place in the other direction.
Try some on your own…
45,700 = 4.57 x 104
0.009 = 9.0 x 10-3
24,200,000 = 2.42 x 107
0.000665 = 6.65 x 10-4
Powers of Ten Video
 Watch the video and complete the section
in the packet.
Converting to Expanded Form
 Move the decimal place the number of
times indicated by the exponent.
 To the right if it is positive.
 To the left if it is negative.
Example:
4.5 x 10-2 = 0.045
Try some on your own…
 1.2 x 10-4 = 0.00012
 9.6 x 103 = 9 600
 8.07 x 102 = 807
Multiplying with Scientific Notation
 Multiply the coefficients
 Add the exponents
Example:
(2.0 x 103) x (2.0 x 103) = 4.0 x 106
Dividing with Scientific Notation
 Divide the coefficients
 Subtract the exponent in denominator from
the numerator.
Example:
3.0 x 104 ÷ 2.0 x 102 = 1.5 x 104-2 = 1.5 x 102
Adding & Subtracting with Scientific
Notation
 In order to add numbers written in scientific
notation, the exponents must match.
Example
5.40 x 103 + 6.0 x 102 =
Change 6.0 x 102 to 0.60 x 103, then add.
5.40 x 103 + 0.60 x 103 = 6.00 x 103
Try some on your own…
(3.95 x 102) ÷ (1.5 x 106) = 2.63 x 10-4
(3.5 x 102) (6.45 x 1010) = 2.2575 x 1013
(4.44 x 107) ÷ (2.25 x 105) = 1.973 x 102
(4.50 x 10-12) (3.67 x 10-12) = 1.6515 x 10-23
A Short History of Standard Units
Humans did not always have standards by which
to measure temperature, time, distance, etc.
It wasn’t until 1790 that France established the
first metric system.
The First Metric System
The French established that one meter
was one ten-millionth of the distance of
the from the Equator to the North Pole.
One second was equal to 1/86,400 of the
average day.
Today’s Standards
The techniques used today to establish standards
are much more advanced than in 1790…
One meter is equal to the distance traveled by light
in a vacuum in 1/299,792,458 of a second.
One second is defined in terms of the number of
cycles of radiation given off by a specific isotope
of the element cesium.
S.I. Units
 The International System of Units is used
ALMOST exclusively worldwide (the U.S.
is one the of the exceptions).
 ALL science is done using S.I. units.
The United States’ System of
Measurement
 In 1975, the U.S.
government
attempted to adopt
the metric system
with little success.
 The U.S. currently
uses the English
System of
Measurement.
Math Quiz
Complete the following:
 3 5/6 in. + 8 4/9 in. + 5 2/7 in. =
Math Quiz
Complete the following:

3.83 cm + 8.44 cm + 5.29 cm =
So why S.I.?
So why S.I.?
 Decimals are more “computationally
friendly”
 Multiples of ten
 Eliminate LARGE numbers by using
prefixes
 Scientifically based
Measurements and SI Units
 Quantitative measurements must include a
number AND a unit.
 Base units are used with prefixes to
indicate fractions or multiples of a unit.
 Try to fill in your table.
Base Units
Base Unit
grams
meter
Liter
Kelvin
degrees Celsius
mole
Symbol
g
m
L
K
°C
mol
second
ampere
candela
Joule
S or sec
A
cd
J
Measures…
mass
distance
volume
temperature
temperature
amount of a
substance
time
electric current
light intensity
energy
Prefixes
 Prefixes combine with base
units to indicate fractions or
multiples of a unit.
Prefixes
Prefix
megakiloHectodecaBase Unit
decicentimillimicronanopicofemto-
Symbol
M
K
H
D
Meaning
d
c
m
µ
n
p
f
10 times smaller than base unit
100 times smaller
1 000 times smaller
1 000 000 times smaller
1 000 000 000 times smaller
1 000 000 000 000 times smaller
1 000 000 000 000 000 times smaller
1 000 000 times larger
1 000 times larger
100 times larger
10 times larger than base unit
SI Prefixes
1 000 000 000 000 000 000 000 000
1 000 000 000 000 000 000 000
1 000 000 000 000 000 000
1 000 000 000 000 000
1 000 000 000 000
1 000 000 000
1 000 000
1 000
100
10
0.1
0.01
0.001
0.000 001
0.000 000 001
0.000 000 000 001
0.000 000 000 000 001
0.000 000 000 000 000 001
0.000 000 000 000 000 000 001
0.000 000 000 000 000 000 000 001
yottazettaexapetateragigamegakilohectodecadecicentimillimicronanopicofemtoattozeptoyocto-
Y
Z
E
P
T
G
M
k
h
da
d
c
m
µ
n
p
f
a
z
y
More Details: Length
 meters
 centimeters (for smaller units of length)
 millimeters (very small units of length)
 kilometers (for large units of length)
These are the most commonly used.
More details: Mass
 gram
 kilogram
Measured using balances.
More details: Volume




liters
milliliters (for small volumes)
microliter (for extremely small volumes)
Measured using a graduated cylinder,
pipet or buret (more accurate), volumetric
flask or even a syringe.
Volume is a derived units…
Some metric units are
derived from S.I. units.
Volume is L x W x H = cm x
cm x cm = cm3
One cm3 is the same as
one mL.
Also, dm x dm x dm = dm3
One dm3 is the same as
one L.
Conversions Using Factor Label
Method
 Multiplying any number by an equality
does NOT change the value.
 An equality is two measurements that are
equal in amount but have different units
and numbers.
 Examples:
one dozen bagels = 12 bagels
10 mm = 1 cm
Steps of Factor Label Method
1. Write down the units you are given.
2. Write X and a Line.
3. Write unit you want to cancel on the
bottom of the line, the unit you want to
keep on the top of the line. Find and plug
in your equality. (hint: the larger unit will
always get a 1 next to it)
4. Cancel units and do the math.
5. Voila!
Let’s do one together…
0.600L = _______mL
1000 mL
0.600L X
= 600 mL
1 L
1 L = 1000mL
TRY THE REST ON YOUR OWN !!!!
Temperature Scales
There are three temperature scales in
use in this country that you need to be
familiar with.
Temperature:
A measure of
the average
kinetic energy
of the particles
in a sample.
Fahrenheit
 18th-century German
physicist Daniel Gabriel
Fahrenheit
 Based his scale on an
ice-salt mixture and
normal body temperature
 Freezing point for water =
32°F
 Boiling point for water =
212°F
Celsius Scale
 Swedish guy, Anders
Celsius in 174
 Freezing point at 0°C.
 Boiling for water at
100°C.
 Below 0 is negative.
Kelvin Scale
 English guy, William
Kelvin
 Measures molecular
movement
 Theoretical point of
ABSOLUTE ZERO is
when all molecular
motion stops (no negative
numbers)
 Divisions (degrees)
are the same as in
Celsius
Absolute Zero
 Theoretical point where there is absolutely
no movement of molecules in matter and a
measure of ZERO ENERGY
 This is not something that we ever
witness, scientists have only theorized this
point
Conversion Factors
 You need to know these conversion
factors!
K = °C + 273
°C = K – 273
On Table T
NOT on
Table T
Practice Conversion Problems
 Room temperature is approximately 23°C. What
is this temperature in Kelvin?
 Ethanol has a boiling point of 351 K. That won’t
help us if we have a thermometer reading
degrees Celsius, so convert it.
Work on the conversion
problems in your packet…
Uncertainty in Measurement
Uncertainty in Measurement
 No measurement can be perfect.
 Scientists need to account for some
degree of uncertainty in measurements.
 Refer to terms accuracy and precision.
 An ideal measuring device is accurate and
precise and does not have a great deal of
uncertainty.
Accuracy
Accuracy is when you are close to the
actual value of what you are trying to
measure (For example you throw three
darts and they are all close to the bull’s
eye).
Precision
Precision is a measure of how close each
measurement is to the others. For example if you
are at the driving range and all of the golf balls
head towards the pond, that is precision (but not
accuracy).
Uncertainty in Measurement
 Uncertainty occurs in every measurement
made and must be accounted for.
In chemistry, we use different tools, each
of which has certain limitations.
We use the ± to indicate uncertainty in
measurement.
Uncertainty Equation
 YOU MUST MEMORIZE THIS EQUATION
AS YOU WILL PERFORM IT ALMOST
DAILY!
ΔF = (δF / δX1) ΔX1 + (δF / δX2) ΔX2 + …(δF / δXn) ΔXn
Just Kidding!
 However, there is a system we use in
chemistry that helps to minimize
uncertainty by only including those values
that have certainty and one that is
uncertain.
We call them SIGNIFICANT FIGURES!
Using Significant Figures
 Why are significant figures important?
 Have you ever multiplied two numbers
and come up with a really LONG decimal?
 Well, those numbers are INSIGNIFICANT
with respect to scientific calculations.
And now for a short story…
Counting Sig Figs
The Atlantic-Pacific Rule
 If the decimal is Absent (A), start
counting on the Atlantic (right)
side. Go to the first NON-zero
number and count everything
after that.
 If the decimal is Present (P), start
counting on the Pacific (left) side.
Go to the first NON-zero number
and count everything after that.
Quick Self-Assessment
 How many sig figs are in each of these numbers:
98,000 m
0.123 L
0.00073 L
8765 cm
40,506 m
20.00 mL
More Practice
 Round each number to the number of sig figs
shown in parentheses.
314.721 m (4)
0.001775 m (2)
8792 m (2)
Sig Figs in Calculations
 When adding or subtracting measurements,
report to the LEAST number of DECIMAL
PLACES.
For example:
12.52 + 349.0 + 8.24 = 369.76
You will report this with one decimal place
as 369.8.
Sig Figs in Calculations
 When multiplying or dividing measurements,
you want to report the answer with the same
number of sig figs as the measurement with
the least number of sig figs.
For example:
7.55 m x 0.34 m = 2.567 square meters
You will report this with 2 sig figs as 2.6 square
meters because 0.34 m contains 2 sig figs.
Percent Error in Experimentation
 When trying to determine how accurate
your experimental value (“what you got in
the lab”) is compared with the theoretical
(“what it is supposed to be”), we use a
simple formula.
 experimental – theoretical x 100%
theoretical
Theoretical
VS
Experimental
% Example of Percent Error %
 When you calculate the density of
chemical X experimentally you get 1.13
g/mL. The actual density according to the
literature is 1.16 g.mL. What is your
percent error?
Density
 Density is a derived unit which is found by
dividing a substances mass by its volume.
Density Equation
D=M/V
Common Units = g/mL or g/cm3
Density Practice Problems
1. A student measures the mass of a piece
of metal to be 4.0g and it has a volume
of 1.5mL what is the density of this
metal?
2. The Density of CO2 gas is 1.8 grams per
liter. What is the mass of 0.2L of CO2
gas?