1 1.3 Measured Numbers and Significant Figures Chapter 1Measurements Copyright © 2009 by Pearson...
-
Upload
melina-nash -
Category
Documents
-
view
214 -
download
0
Transcript of 1 1.3 Measured Numbers and Significant Figures Chapter 1Measurements Copyright © 2009 by Pearson...
1
1.3Measured Numbers and
Significant Figures
Chapter 1 Measurements
Copyright © 2009 by Pearson Education, Inc.
2
Measured Numbers
A measuring tool
• is used to determine a quantity such as height or the mass of an object.
• provides numbers for a measurement called measured numbers. Copyright © 2009 by Pearson Education, Inc.
3
. 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 may be estimated between 2.7–
2.8 as half way (0.5) or a little more (0.6), which gives a reported length of 2.75 cm or 2.76 cm.
Reading a Meterstick
4
Known & Estimated Digits
If the length is reported as 2.76 cm,
• the digits 2 and 7 are certain (known).• the final digit, 6, is estimated (uncertain).• all three digits (2, 7, and 6) are significant, including
the estimated digit.
5
. l8. . . . l . . . . l9. . . . l . . . . l10. . cm
What is the length of the orange line?
1) 9.0 cm
2) 9.04 cm
3) 9.05 cm
Learning Check
6
. l8. . . . l . . . . l9. . . . l . . . . l10. . cm
The length of the orange line could be reported as
2) 9.04 cm
or 3) 9.05 cm
The estimated digit may be slightly different. Both readings are acceptable.
Solution
7
. l3. . . . l . . . . l4. . . . l . . . . l5. . cm
• For this measurement, the first and second known digits are 4 and 5.
• When a measurement 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
8
Significant Figures in Measured Numbers
Significant Figures
• obtained from a measurement include all of the known digits plus the estimated digit.
• reported in a measurement depend on the measuring tool.
9
Significant Figures
10
All nonzero numbers in a measured number are significant.
Number of Measurement Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb 3
122.55 m 5
Counting Significant Figures
11
Sandwiched Zeros• occur between nonzero numbers.• are significant.
Number of Measurement Significant Figures50.8 mm 32001 min 40.0702 lb 30.405 05 m 5
Sandwiched Zeros
12
Trailing Zeros• follow nonzero numbers in numbers without
decimal points.• are usually placeholders. • are not significant.
Number of Measurement Significant Figures25 000 cm 2
200 kg 1 48 600 mL 3
25 005 000 g 5
Trailing Zeros
13
Leading Zeros • precede nonzero digits in a decimal number. • are not significant.
Number of Measurement Significant Figures0.008 mm 10.0156 oz 30.0042 lb 20.000 262 mL 3
Leading Zeros
14
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
15
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
16
Significant Figures in Scientific Notation
In scientific notation all digits in the coefficient
including zeros are significant.
Number of Measurement Significant Figures
8 x 104 m 1
8.0 x 104 m 2
8.00 x 104 m 3
17
Study Tip: Significant Figures
The significant figures in a measured number are• all the nonzero numbers.
12.56 m 4 significant figures• zeros between nonzero numbers.
4.05 g 3 significant figures• zeros that follow nonzero numbers in a decimal
number.25.800 L 5 significant figures
18
A. Which answer(s) contain 3 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 (1). 2) two (2). 3) three (3).
Learning Check
19
A. Which answer(s) contain 3 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 (3).
Solution
20
In which set(s) do both numbers contain the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000 015 and 150 000
Learning Check
21
Solution
In which set(s) do both numbers contain the same number of significant figures?
3) 0.000 015 and 150 000
Both numbers contain 2 significant figures.
22
Examples of Exact Numbers
An exact number is obtained
• when objects are counted. Counted objects
2 soccer balls4 pizzas
• from numbers in a defined relationship. Defined relationships
1 foot = 12 inches1 meter = 100 cm
23
Exact Numbers
24
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.
25
Solution
A. Exact numbers are obtained by
2. counting.
3. definition.
B. Measured numbers are obtained by
1. using a measuring tool.
26
Learning Check
Classify each of the following as (1) exact or (2) measurednumbers.
A.__Gold melts at 1064 °C.
B.__1 yard = 3 feet
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.
27
Classify each of the following as (1) exact or (2) measurednumbers.
A. 2 A measuring tool is required.
B. 1 This is a defined relationship.
C. 2 A measuring tool is used to determine
length.
D. 1 The number of hats is obtained by counting.
E. 2 The volume of soda is measured.
Solution