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Welcome to
Honors Chemistry
Ms. O’Neill
Summer Topics
• Units of Measure Review
• Scientific Notation Review
• Intro to Significant Figures
• Background work for Dimensional Analysis Success
Units of Measurement and Their
Abbreviations
Volume
Useful relationships between units of volume
include:
1 m3 = 1000 L
1 L = 1000 mL
1 mL = 1 cm3
1 L = 1.057 qt
946.3 mL = 1 qt
© 2014 Pearson Education, Inc.
Scientific Notation
Scientific notation is used to write very large or very small numbers such as
• the width of a human hair,
0.000008 m, which is also
written as 8 × 10−6 m
• the number of hairs on a
human scalp,100000,
which is also written as 1 × 105 hairs
© 2014 Pearson Education, Inc.
Writing Numbers in Scientific Notation
• A number written in scientific notation contains a
coefficient and a power of ten.
coefficient
power unit
of ten
1.5 × 102
m
• The coefficient is at least 1 but less than 10.
© 2014 Pearson Education, Inc.
Writing Numbers in Scientific Notation
• The number of spaces moved to obtain a coefficient between 1
and 10 is shown as a power of ten.
52 000. = 5.2 × 104
move decimal 4 spaces left
0.003 78 = 3.78 × 10−3
move decimal 3 spaces right
© 2014 Pearson Education, Inc.
Measured Numbers
A measuring tool
• is used to determine a quantity such as the length
or the mass of an object
• provides numbers for a measurement called
measured numbers
Basic Chemistry
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Copyright © 2011 Pearson Education, Inc.
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Reading a Meterstick
. l2. . . . l . . . . l3 . . . . l . . . . l4. . cm
• The markings on the meterstick at the end of the
orange line are read as
The first digit
2
plus the second digit 2.7
• The last digit is obtained by estimating.
• The end of the line might be estimated between 2.7–
2.8 as half-way (0.05) or a little more (0.06), which
gives a reported length of 2.75 cm or 2.76 cm.
Basic Chemistry
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Known + Estimated Digits
In the length reported as 2.76 cm,
• the digits 2 and 7 are certain (known)
• the final digit 6 was estimated (uncertain)
• all three digits (2.76) are significant including the
estimated digit
Basic Chemistry
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Learning Check
. l8. . . . l . . . . l9. . . . l . . . . l10. .
cm
What is the length of the red line?
1) 9.0 cm
2) 9.03 cm
3) 9.04 cm
Basic Chemistry
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Solution
. l8. . . . l . . . . l9. . . . l . . . . l10. . cm
The length of the red line could be reported as
2) 9.03 cm
or
3) 9.04 cm
The estimated digit may be slightly different. Both
readings are acceptable.
Basic Chemistry
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Zero as a Measured Number
. l3. . . . l . . . . l4. . . . l . . . . l5. . cm
• For this measurement, the first and second known digits
are 4.5.
• Because the line ends on a mark, the estimated digit in
the hundredths place is 0.
• This measurement is reported as 4.50 cm.
Basic Chemistry
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Significant Figures in Measured Numbers
• Significant figures obtained from a measurement include all of the known
digits plus the estimated digit.
• The number of significant figures reported in a measurement depends on
the measuring tool.
Basic Chemistry
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Significant Figures – please memorize
Basic Chemistry
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Counting Significant Figures
All nonzero numbers in a measured number are significant.
Measurement
38.15 cm
5.6 ft
65.6 lb
122.55 m
Basic Chemistry
Number of
Significant Figures
4
2
3
5
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Sandwiched Zeros
Sandwiched zeros
• occur between nonzero numbers
• are significant
Measurement
50.8 mm
2001 min
0.0702 lb
0.40505 m
Basic Chemistry
Number of Significant
Figures
3
4
3
5
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Trailing Zeros
Trailing zeros
• follow nonzero numbers in numbers without decimal
points
• are placeholders
• are not significant
Measurement
25 000 cm
200 kg
48 600 mL
25 005 000 g
Basic Chemistry
Number of Significant
Figures
2
1
3
5
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Leading Zeros
Leading zeros
• precede nonzero digits in a decimal number
• are placeholders
• are not significant
Measurement
0.008 mm
0.0156 oz
0.0042 lb
0.000262 mL
Number of Significant Figures
1
3
2
3
Basic Chemistry
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Significant Figures in Scientific Notation
In scientific notation
• all digits including zeros in the coefficient are significant
Scientific Notation Number of
Significant Figures
8 x 104 m
1
8.0 x 104 m
2
8.00 x 104 m
3
Basic Chemistry
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Learning Check
State the number of significant figures in each
of the following measurements:
A.
0.030 m
B.
4.050 L
C.
0.0008 g
D.
2.80 m
Basic Chemistry
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Solution
State the number of significant figures in each of the
following measurements:
A. 0.030 m
2
B. 4.050 L
4
C. 0.0008 g
1
D. 2.80 m
3
Basic Chemistry
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Learning Check
A. Which answer(s) contain three significant figures?
1) 0.4760 2) 0.00476
3) 4.76 x 103
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. The number of significant figures in 5.80 x 102 is
1) one
3) two
3) three
Basic Chemistry
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Solution
A. Which answer(s) contain three significant figures?
2) 0.00476
3) 4.76 x 103
B. All the zeros are significant in
2) 25.300
3) 2.050 x 103
C. The number of significant figures in 5.80 x 102
is
3) three
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
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Learning Check
In which set(s) do both numbers contain the
same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 4.00 x 102
3) 0.000015 and 150,000
Basic Chemistry
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Solution
In which set(s) do both numbers contain the same number of
significant figures?
3) 0.000015 and 150,000
Both numbers contain two (2) significant figures.
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
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Exact Numbers – have INFINITE amount of
Significant Figures
An exact number is obtained
• when entire objects are counted
Example: counting objects
2 baseballs
4 pizzas
• from numbers in a defined relationship
Example: defined relationships
1 foot = 12 inches
1 meter = 100 cm
Basic Chemistry
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Examples of Exact Numbers
Basic Chemistry
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Learning Check
A. Exact numbers are obtained by
1. using a measuring tool
2. counting
3. definition
B. Measured numbers are obtained by
1. using a measuring tool
2. counting
3. definition
Basic Chemistry
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Solution
A. Exact numbers are obtained by
2. counting
3. definition
B. Measured numbers are obtained by
1. using a measuring tool
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
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Learning Check
Classify each of the following as exact (E) or
measured numbers (M). Explain your answer.
A.__Gold melts at 1064 °C.
B.__1 yd = 3 ft
C.__The diameter of a red blood cell is 6 x 104 cm.
D.__There are 6 hats on the shelf.
E.__A can of soda contains 355 mL of soda.
Basic Chemistry
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Solution
Classify each of the following as exact (E) or
measured numbers (M).
A. M A measuring tool is required.
B. E This is a defined relationship.
C. M A measuring tool is used to determine
length.
D. E The number of hats is obtained by counting.
E. M The volume of soda is measured.
Basic Chemistry
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Dimensional Analysis
• Is the chemist’s way of working chemistry problems that are
mathematical in nature.
• Some memorization is vital to the method
• Learning the method saves time
Dimensional Analysis and Conversions
• Metric conversions are all based on factors of 10 and prefixes.
• Metric System: know the required prefixes, meanings and values for any
base unit of measure
You are asked to memorize one particular way
Base Unit: gram Abbreviation: g
1 kg = 1000g
1 g = 10 dg = 100 cg = 1000 mg = 1x106 µg = 1x109ng
Basis for Dimensional Analysis: ONE
• Multiplying by one does not change a value
• More than one way to multiply by one!
• What is
•
𝑎
𝑎
𝑎
=?
𝑎
=1
• What about if a = b…what is
𝑎
𝑏
• =1 AND
𝑏
=1
𝑎
𝑎
=?
𝑏
• So you can multiply something by an equality fraction and not change
the innate value