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Transcript of 2 3 measured_number_and_sig
1
2.3
Measured Numbers and Significant Figures
Chapter 2 Measurements
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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 Copyright © 2011 Pearson Education, Inc.
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. 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.
Reading a Meterstick
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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 Copyright © 2011 Pearson Education, Inc.
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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 Copyright © 2011 Pearson Education, Inc.
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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.
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. 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.
Zero as a Measured Number
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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Significant Figuresin 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.
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Significant Figures
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All nonzero numbers in a measured number are significant.
Measurement Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb 3
122.55 m 5
Counting Significant Figures
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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Sandwiched zeros• occur between nonzero numbers• are significant
Measurement Number of Significant Figures
50.8 mm 32001 min 40.0702 lb 30.40505 m 5
Sandwiched Zeros
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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Trailing zeros
• follow nonzero numbers in numbers without decimal points
• are placeholders
• are not significant
Measurement Number of Significant Figures
25 000 cm 2 200 kg 1 48 600 mL 3
25 005 000 g 5
Trailing Zeros
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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Leading zeros • precede nonzero digits in a decimal number• are placeholders• are not significant
Measurement Number of Significant Figures
0.008 mm 10.0156 oz 30.0042 lb 20.000262 mL 3
Leading Zeros
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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 Copyright © 2011 Pearson Education, Inc.
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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
Learning Check
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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
Solution
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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
Learning Check
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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
Solution
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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
Learning Check
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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.
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Exact Numbers
An exact number is obtained • when objects are counted
Example: counting objects2 baseballs4 pizzas
• from numbers in a defined relationshipExample: defined relationships
1 foot = 12 inches1 meter = 100 cm
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Examples of Exact Numbers
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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
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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
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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 104 cm.
D.__There are 6 hats on the shelf.
E.__A can of soda contains 355 mL of soda.
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
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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.
Solution
Basic Chemistry Copyright © 2011 Pearson Education, Inc.