Honors Chemistry
Chapter 3 Notes – Scientific Measurement
(Student edition)
Chapter 3 problem set: 57-61, 64, 65, 70, 71, 76, 84, 86, 89, 92, 101, 106
Useful diagrams:
3.5, 3.6, 3.9, 3.13
3.1 Measurements and Their Uncertainty
Measurement: a quantity that has both a
and a
.
Measurements are fundamental to the experimental sciences. For that reason, it is
important to be able to make measurements and to decide whether a measurement
is correct.
Scientific Notation: a given number is written as the product of two numbers: a
coefficient and 10 raised to a power.
Accuracy: is a measure of how close a measurement comes to the actual or true
value of whatever is measured.
Precision: is a measure of how close a series of measurements are to one another.
Precise
Accurate
Accurate and Precise
:
Experiments don’t always give perfect results. Error is pretty much a given.
Observed Value (Experimental Value): the
True Value (Accepted Value, Theoretical Value): the
– typically found in a resource.
Absolute Error: the
Percent Error
value in the lab.
value
between the true and observed value.
=
The order is important. It implies direction. + or - shows the direction of
the error. It indicates if values are either too high or too low.
1
Percent error should be treated as absolute value. Looking at the absolute
error in terms of + or – can help you to better analyze your experiments.
Example: 65 oC is the answer in your experiment. 66 oC is the
theoretical value. Calculate the percent error.
NIB - Uncertainty in Measurement:
Two important points to remember regarding measurement:
1. Instruments can only measure so well.
2. We only need some measurements to be really exact.
A person has a height of 5’ 11” inches, not 5.916666667 feet.
When measuring, include all readable digits and one
0 cm
1
digit.
2
If the measurement is exactly half way between lines record it as
If it is a little over, record
If it is a little under, record
Significant Figures (Digits) - “Sig Figs”:
Significant Figures: includes all of the digits that are
plus a last digit that is
.
,
Measurements must always be reported to the correct number of
significant figures because calculated answers often depend on the number
of significant figures in the values used in the calculation.
Example: say you collect a paycheck for a 40 hour week. How much
difference is there between getting paid pi vs. 3.14 per hour?
40 x pi = $
40 x 3.14 = $
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Rules for finding the # of sig figs:
1. All non-zeros are significant
Examples:
2. Zeros between non-zeros are significant
Examples:
3. All other zeros are significant only if....
a) they are to the right or left of decimal point
and
b) they are to the right of a sig fig
- all other (not a and b) are simply place holders
Examples:
Let’s sing the sig fig song!!!!
Sig figs apply to scientific notation as well:
Examples:
Calculating with Measurements ( Sig Fig Math )
In general, a calculated answer cannot be more accurate than the least
accurate measurement from which it was calculated.
Rules of Rounding:
numbers greater than 5 (6-9) get rounded up
numbers less than 5 (1-4) get rounded down
for numbers ending on 5 (the “5” rule):
if the preceding digit is odd, round up
if the preceding digit is even, round down
Round the following examples to 3 sig figs:
35.27

87.24

35.25

95.15

3
* The “5” rule only applies to a “dead even” 5. If any digit other than 0 follows a 5 to be
rounded, then the number gets rounded up without regard to the previous digit.
Round the following examples to 3 sig figs:35.25000000000000000000001 
Rules for calculating with sig figs:
1. When multiplying or dividing, the answer should have the
smaller # of sig figs in the original problem.
Example:
2 x 4.001283 doesn’t equal
2 x 4.001283 =
Example:
3.9577836
15 divided by 3.79 doesn’t equal
15 divided by 3.79 =
2. When adding or subtracting, round to the last common decimal place on
the right.
Example:
21.52 + 3.1 doesn’t equal
21.52 + 3.1 =


Exact conversion factors do not limit the # of sig figs. The final answer should
always end with the # of sig figs that started the problem.
Let’s refer back to sig figs and percent error now…
NIB - Use of +/- notation:
Scientists sometimes use +/- notation to show how much uncertainty there
is in a measurement.
46.85 mm +/- .03 mm
This means that the answer could be as high as ___________ mm or as
low as __________ mm.
Of course, there is always implied uncertainty. If we say a building is 9 m
high, we’re saying that it is between 8 and 10 m high. We say 9 because
it’s closer to 9 than 8 and closer to 9 than 10. We report 9 +/- .5 m
Measurement
900
90
9
9.0
9.00
900.
900.0
Implied Range
+/+/+/+/+/+/+/-
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3.2
International System of Units
SI system: Le Systeme International d’Unites: 7 base units
Quantity
Length
Mass
Temperature
Time
Amount of Substance
Luminous Intensity
Electric Current
SI Base Unit
Meter
Kilogram
Kelvin
Second
Mole
Candela
Ampere
Symbol
m
kg
K
s
mol
cd
A
SI Advantages: easily convertible using decimals. English system uses fractions.
Prefixes to know:
Prefix
Giga
Mega
Kilo
Deca
Deci
Centi
Milli
Micro
Nano
Pico
Symbol Value
G
M
K
da
d
c
m
µ
n
p
0.000 000 001
0.000 001
0.001
0.1
10
100
1000
1,000,000
1,000,000,000
1,000,000,000,000
Base Unit
Value
1
1
1
1
1
1
1
1
1
1
Units of Volume:
Volume = length x width x height
1 cm3 = 1 mL
1 dm3 = 1 L
Volume is a derived unit.
Derived Units: a combination of units.
Other derived units: area  cm2
Density  g/cm3
Speed  m/s
5
Units of Temperature:
Temperature is used to determine the direction of heat transfer.
Temperature is measured in degrees
Temperature (definition):
Thermometer - works by thermal expansion - usually Hg or alcohol
Temperature scales
Celsius - devised by a Swedish astronomer - Anders Celsius - 1742
Kelvin - named for Lord Kelvin - English physicist
absolute zero - temperature at which all molecular motion stops temperature =
0 K or -273.15 Co
It’s never been reached, but we have gotten within 1/1,000,000,000 K.
Conversion formulas
K = Co + 273
**Fo = 9/5(Co)
+ 32
**Co = 5/9(Fo - 32)
** ask about the coolest rule ever
Units of Energy:
Energy: The capacity to do work or to produce heat.
1 Joule = 0.2390 calories
1 cal = 4.184 J
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3.3
Conversion Problems
General Rules for Problem Solving:
1. Read the problem - make a list of knowns and unknowns
2. Look up any needed information (conversion factors, etc.)
3. Work out a plan.
4. Do the math.
5. Check your work. Does the answer seem right? Did you record the correct
number of sig figs? Does your answer have the proper unit?
Conversion Factor: a ratio of equivalent measurements.
Dimensional Analysis (Factor Label Method): a method of problem solving that
treats units like algebraic factors.
Basic Rules:
1. Put the known quantity over the number 1.
2. On the bottom of the next term, put the unit on top of the
previous term.
3. On top of the current term put a unit that you are trying to get to.
4. On the top and bottom of the current term, put in numbers in
order to create an equality.
5. If the unit on top is the unit of your final answer,
multiply/divide and cancel units. If not, return to step # 2.
6. As far as sig figs are concerned, end with what you start with!
Example: convert 3.0 ft to inches
Example: convert 1.8 years to seconds
Example: convert 2.50 ft to cm if 1 inch = 2.54 cm
Example: convert 0.75 L to cm3
Example: convert 1,500,000,000 mm3 to m3
Example: convert 22 cm to dm
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3.4
Density
Density: the ratio of the
of an object to its
.
D=
Density is an intensive property that depends only on the
a substance, not on the
of the sample.
The density of a substance generally
of
as its temperature increases.
Careers in Chemistry:
Analytical chemists focus on making quantitative measurements. They can work for a
pharmaceutical company investigating the composition of medicines in drugs. They are
creative thinkers and find solutions to problems. They can also be hired by biomedicine
companies, biochemistry companies, and industrial manufacturers. Many of these jobs
require a master’s degree or Ph. D.
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