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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Chapter 2 – Measurements and Solving Problems
2.1 Units of Measurement
Problem Set: 14-19, 22-25, 29-31, 35-44
Steps of the Scientific Method
1. _____________ - state it clearly – usually as a question
2. ____________________ - do some research on your problem
3. ________________ - a suggested solution
4. __________________ - experiment and examine the situation to check the hypothesis
5. ____________ - Note everything your senses can gather. Record the data and keep careful records.
6. _________________ - Put the data in order- charts/tables. Figure out the meaning of the data
7. __________________ - Explain the data. State whether or not it supports the hypothesis.
Additional Definitions
__________ - A hypothesis that has been rigorously tested, and not found faulty, usually also
having been found somewhat useful.
__________ - A readily demonstrable fact that cannot be disproven
Units of Measurement
Measurement – _______________________________________________________________________
The problem is, what do you use as a standard?
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Standard should be an object or natural phenomenon of constant value, easy to preserve and
reproduce, and practical in size.
The SI System
SI =
Important base units to know:
Quantity
Unit
Abbreviation
Mass
Length
Volume
Time
Temperature
Amount of substance
Important prefixes(multiples of base units) to know:
Prefix
Abbreviation
Meaning
Example
tera
1012
1 terameter =
giga
109
1 gigameter =
mega-
106
1 megameter =
kilo-
103
1 kilogram =
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
hecto-
102
1 hectometer =
deka
101
1 dekameter =
BASE
deci-
10-1
1 deciliter
centi-
10-2
1 centimeter =
milli-
10-3
1 millimeter=
micro-
10-6
1 micrometer =
nano-
10-9
1 nanometer =
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
pico-
10-12
1 picometer =
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Significant Figures (Digits) - “Sig Figs”

Definition: _____________________________________________________________________
1.15 ml implies 1.15 + 0.01 ml

The more significant digits, the more reproducible the measurement is.
These are the numbers that “count!”
Ex1:
 = 22/7 = 3.1415927
what do math teachers let you use?
Ex2: You collect a paycheck for a 40 hour week – what’s the difference between getting paid pi vs. 3.14 ?
Rules for finding the # of sig figs
1. All non-zeros are significant
ex.
7 [
2. Zeros between non-zeros are significant
ex.
707 [
]
77 [
]
]
7053 [
]
4568 [
]
7.053 [
]
3. Zeroes to the left of the first nonzero digit fix the position of the decimal point and are not significant
ex:
0.0056 [
]
0.0789 [
]
0.0000001 [
]
4. In a number with digits to the right of a decimal point, zeroes to the right of the last nonzero digit are
significant
ex:
43 [
]
43.00 [
]
43.0 [
]
0.00200 [
] 0.040050 [
]
5. In a number that has no decimal point, and that ends in zeroes (ex. 3600), the zeroes at the end may or
may not be significant (it is ambiguous). To avoid ambiguity, express in scientific notation and show in the
coefficient the number of significant digits.
ex. 3600 = 3.6 x 103 [ ]
Scientific Notation
•
A way to express very small or very large numbers
•
Examples:
•
56934 =
•
0.0000037 =
•
2.347 x 10-3 =
•
8.98736 x 105 =
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Counting significant digits
1. __________________________________________________________
2. __________________________________________________________
Ex1:
700
[
]
- means “about 700 people at a football game”
700.
[
]
- means “exactly 700 ......”
700.0
[
]
- means “teacher weighs exactly 700.0 lbs”
Other examples
0.5 [
]
0.50 [
]
0.050 [
]
Sig. figs apply to scientific notation as well
9.7 x 10 2 = 970
[
]
1.20 x 10 -4 = .000120
[
]
Calculating with Measurements ( Sig Fig Math )
Rounding Rules
XY ---------------------> Y
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________
_____________________________________________
Ex1: round to 3 sig figs
35.27 =
87.24 =
95.25 =
95.15 =
Note - 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.
Ex2: round to 3 sig figs
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35.250000000000000000000000001
=
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Calculating rules:
1. Multiplying or dividing – round results to the smaller # of sig. figs in the original problem.
Ex1:
3.10
cm
4.102 cm
x 8.13124 cm
Ex2:
7.9312 g
/ 0.98 m
2. Adding or subtracting - round to the last common decimal place on the right.
Ex1:
21.52
+ 3.1?
Ex2:
73.01234 g
- 73.014?? g
Note - 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
ex. convert 7866 cm
to m
Partner Share:
How do you determine the proper sig figs when adding and subtracting?
How do you determine the proper sig figs when multiplying or dividing?
What is the 5 rule?
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Factor Label Method (Dimensional Analysis)
A method of problem solving that treats units like algebraic factors

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 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!
Ex1 - convert 26 inches to feet
Ex2 - convert 1.8 years to seconds
Ex3 - convert 2.50 ft to cm if 1 inch = 2.54 cm
Ex4 - convert 150 g
to
ug
Ex5 - convert 75 cm
to
Hm
Ex6 - convert 0.75 L
to
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cm3
(1 cm3 = 1 mL)
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Density – ratio of mass to volume
Partner Share
What do you know about density? When you are writing about it, include an example of
density using water and oil.
The common density units are:



Formula is _________________________________
Density is a)
b)
c)
Two ways to find volume in density problems:
1.
2.
Note: the density is the same no matter what is the size or shape of the sample.
Ex1: Find the density of an object with m= 10g and v=2 cm 3
Ex2: A cube of lead 3.00 cm on a side has a mass of 305.0 g. What is the density of lead?
First, calculate it’s volume:
Next, calculate the density:
Ex 3: A graduated cylinder contains 25 mL of water. When a 4.5 g paper clip is dropped into the water,
the water level rises to 36 mL. What is the density of the paper clip?
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
2.3 Using Scientific Measurement
Precision vs. Accuracy
Precision
Accuracy







 s
good precision & good accuracy
poor accuracy but good precision
good accuracy but poor precision
poor precision & poor accuracy
Partner Share
Explain the difference between precision and accuracy.
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Percent Error - experiments don’t always give true results - error is pretty much a given
Observed value (experimental value) - data found in an experiment
True value (accepted value, theoretical value) - data that is generally accepted as true
Percent (%) error =
(order is important as it implies direction)
+/- shows the direction of the error - values are either too high or too low
Ex1: 66 Co is the answer in your experiment
65 CO is the theoretical value
Partner Share
What lab results would give you a positive percent error?
What lab results would give you a negative percent error?
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Accelerated Chemistry
Chapter 2 Notes – Measurements and Solving Problems
Uncertainty in Measurement

making a measurement usually involves comparison with a unit or a scale of units

Two important points:
1. ______________________________________________________________________________
2. ______________________________________________________________________________

When making a measurement, include all readable digits and 1 estimated digit
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o
always read between the lines!
o
the digit read between the lines is always uncertain

if the measurement is exactly half way between lines record it as 0.5

if it is a little over, record ___________________

if it is a little under, record __________________

You would read this as 18.0 mL and not 18.5 mL.
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