Section 2.2 Section 2.2 Scientific Notation and Dimensional Analysis Section 2-2 • Express numbers in scientific notation. • Convert between units using dimensional.
Download ReportTranscript Section 2.2 Section 2.2 Scientific Notation and Dimensional Analysis Section 2-2 • Express numbers in scientific notation. • Convert between units using dimensional.
Slide 1
Section 2.2
1
Slide 2
Section 2.2 Scientific Notation and Dimensional Analysis
Section 2-2
• Express numbers in scientific notation.
• Convert between units using dimensional analysis.
quantitative data: numerical information describing
how much, how little, how big, how tall, how fast, and
so on
Slide 3
Section 2.2 Scientific Notation and Dimensional Analysis (cont.)
Section 2-2
scientific notation
dimensional analysis
conversion factor
Scientists often express numbers in scientific
notation and solve problems using
dimensional analysis.
Slide 4
Scientific Notation and Dimensional Analysis
Standard I&E: 1e
Terms: 31
Mastering Concepts: 50 (58-61)
Practice Problems: 32(12-14),33(15-16)34(17),35(1921)
Homework:
Cornell Notes: 2.2
Section Assessment: 35(22-26)
Mastering Problems: 50 (75-80)
10 Stamps
4
Slide 5
Metric System
Prefixes convert the base units into units that are
appropriate for the item being measured.
5
Slide 6
SI Units
• Système International d’Unités
• Uses a different base unit for each quantity
6
Slide 7
Scientific Notation
Section 2-2
• Scientific notation can be used to express
any number as a number between 1 and 10
(the coefficient) multiplied by 10 raised to a
power (the exponent).
• Count the number of places the decimal
point must be moved to give a coefficient
between 1 and 10.
Slide 8
Scientific Notation (cont.)
Section 2-2
• The number of places moved equals the
value of the exponent.
• The exponent is positive when the
decimal moves to the left and negative
when the decimal moves to the right.
800 = 8.0 102
0.0000343 = 3.43 10–5
Slide 9
Scientific Notation (cont.)
Section 2-2
• Addition and subtraction
– Exponents must be the same.
– Rewrite values with the same
exponent.
– Add or subtract coefficients.
Slide 10
Scientific Notation (cont.)
Section 2-2
• Multiplication and division
– To multiply, multiply the coefficients, then add the
exponents.
– To divide, divide the coefficients, then subtract the
exponent of the divisor from the exponent of the
dividend.
Slide 11
Dimensional Analysis
Section 2-2
• Dimensional analysis is a systematic
approach to problem solving that uses
conversion factors to move, or convert,
from one unit to another.
• A conversion factor is a ratio of equivalent
values having different units.
Slide 12
Dimensional Analysis (cont.)
Section 2-2
• Writing conversion factors
– Conversion factors are derived from
equality relationships, such as 1
dozen eggs = 12 eggs.
– Percentages can also be used as
conversion factors. They relate the
number of parts of one component
to 100 total parts.
Slide 13
Dimensional Analysis (cont.)
Section 2-2
• Using conversion factors
– A conversion factor must cancel one unit and
introduce a new one.
Slide 14
Sec. 2.2 Cornell Notes
Summary
Scientists often
express numbers in
scientific notation and
solve problems using
dimensional analysis.
2.2 Scientific Notation and Dimensional
Analysis
• Scientific notation makes it easier to handle
extremely large or small measurements.
• Numbers expressed in scientific notation are
a prod- uct of two factors: (1) a number
between 1 and 10 and (2) ten raised to a
power.
• Numbers added or subtracted in scientific
notation must be expressed to the same
power of ten.
• When measurements are multiplied or
divided in scientific notation, their exponents
are added or subtracted, respectively.
• Dimensional analysis often uses conversion
factors to solve problems that involve units.14A
Slide 15
Standard: I&E
1.e Solve scientific problems by using
quadratic equations and simple
trigonometric, exponential, and
logarithmic functions.
Vocabulary
scientific notation
conversion factor
dimensional analysis
15
Slide 16
Mastering Concepts: 50 (58-61)
Slide 17
Mastering Concepts: 50 (58-61)
58. How does scientific notation differ from ordinary
notation? (2.2)
Scientific notation uses a number between 1 and 10
times a power of ten to indicate the size of very large
or small numbers.
59. If you move the decimal place to the left to convert
a number into scientific notation, will the power of ten
be positive or negative? (2.2)
positive
60. When dividing numbers in scientific notation, what
must you do with the exponents? (2.2)
Subtract them.
61. When you convert from a small unit to a large unit,
what happens to the number of units? (2.2)
17
It decreases.
Slide 18
Significant Figures:
Rules for counting significant figures
All nonzero numbers count
Leading zeros don’t count
Trailing zeros count if there is a decimal
Trailing zeros don’t count if there is no decimal
18
Slide 19
Practice Problems: 32(12-13)
12.Express the following quantities in scientific
notations:
a) 700 m
b) 38 000m
c) 4 500 000 m
d) 685 000 000 000 m
e) 0.0054 kg
f) 0.000 006 87 kg
g) 0.000 000 076 kg
h) 0.000 000 000 8 kg
19
Slide 20
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
a. 700 m
700.
= 7 X 102 m
20
Slide 21
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
b. 38 000 m
38000.
3.8 X 104 m
21
Slide 22
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
c. 4 500 000 m
4 500000
4.5 X 106 m
22
Slide 23
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
d. 685 000 000 000 m
685000000000
6.85 X 1011 m
23
Slide 24
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
e. 0.0054 kg
0.0054
5.4 X 10-3 kg
24
Slide 25
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
f. 0.000 006 87 kg
0.000 006 87
6.87 X 10-6 kg
25
Slide 26
Your Turn
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
g. 0.000 000 076 kg
h. 0.000 000 000 8 kg
26
Slide 27
Practice Problems: 32(12-13)
13. Express the following quantities in scientific
notations:
a.
b.
c.
d.
360 000 s
0.000 054 s
5060 s
89 000 000 000 s
27
Slide 28
13.
Express the following quantities in scientific
notation.
a. 360 000 s
360 000
3.6X105s
28
Slide 29
13.
Express the following quantities in scientific
notation.
b. 0.000 054 s
0.000 054
5.4 X10-5 s
29
Slide 30
Your Turn
13.
Express the following quantities in scientific
notation.
c. 5060 s
d. 89 000 000 000 s
30
Slide 31
Rules for calculating with significant figures:
• Addition and Subtraction: You are only as
good as your least accurate place value
31
Slide 32
Practice Problems: 32 (14)
Solve the following addition and subtraction problems.
Express your answers in scientific notation.
a. 5 x 10 -5 m + 2 x 10-5 m
b. 7 x 10 8 m - 4 x 10 8 m
c. 9 x 10 2 m - 7 x 10 2 m
d. 4 x 10 -12 m + 1 x 10 -12 m
e. 1.6 x 104 kg + 2.5 x 103 kg
f. 7.06 x 10-3 kg + 1.2 x 10-4 kg
g. 4.39 x 105 kg - 2.8 x 104 kg
h. 5.36 x 10-1 kg – 7.40 x 10-2 kg
32
Slide 33
Practice Problems: 32 (14)
Solve the following addition and subtraction
problems. Express your answers in scientific
notation.
a. 5 x 10 -5 m + 2 x 10-5 m =
7x10-5 m
b. 7 x 10 8 m - 4 x 10 8 m=
3x108m
33
Slide 34
Practice Problems: 32 (14)
Solve the following addition and subtraction
problems. Express your answers in scientific
notation.
c. 9 x 10 2 m - 7 x 10 2 m=
2x102m
d. 4 x 10 -12 m + 1 x 10 -12 m=
5x10-12 m
34
Slide 35
e. 1.6 x 104 kg + 2.5 x 103 kg=
1.6 x 104 kg + 0.25 x 104 kg=
1.85x104 m
f. 7.06 x 10-3 kg + 1.2 x 10-4 kg=
7.06 x 10-3 kg + 0.12 x 10-3 kg=
7.18 x 10-3 kg
35
Slide 36
g. 4.39 x 105 kg - 2.8 x 104 kg=
4.39 x 105 kg – 0.28 x 105 kg=
4.11 x 105 kg
h. 5.36 x 10-1 kg – 7.40 x 10-2 kg=
5.36 x 10-1 kg – 0.740 x 10-1 kg=
4.62 x 10-1 kg
36
Slide 37
Rules for calculating with significant figures:
• Multiplication and Division: You are only as
good as your least accurate number of
significant figures
37
Slide 38
Practice Problems: 33 ( 15-16)
15. Calculate the following areas. Report the
answers in square centimeters, cm2
a. (4 x 102 cm ) X (1 x 108 cm)
b. (2 x 10-4 cm ) X (3 x 102 cm)
c. (3 x 101 cm ) X (3 x 10-2 cm)
d. (1 x 103 cm ) X (5 x 10-1 cm)
38
Slide 39
Practice Problems: 33 ( 15-16)
15. Calculate the following areas. Report the
answers in square centimeters, cm2
a. (4 x 102 cm ) X (1 x 108 cm)
4 x 1010 cm2
b. (2 x 10-4 cm ) X (3 x 102 cm)
6 x 10-2 cm2
39
Slide 40
Practice Problems: 33 ( 15-16)
15.Calculate the following areas. Report the
answers in square centimeters, cm2
c. (3 x 101 cm ) X (3 x 10-2 cm)
9 x 10-1 cm2)
d. (1 x 103 cm ) X (5 x 10-1 cm)
5 x 102 cm2
40
Slide 41
Practice Problems: 33 ( 15-16)
16. Calculate the following densities. Report the
answers in g/cm3
a. (6 x 102 g) ÷ (2x 101 cm3 )=
3 x 101 g/cm3
b. (8 x 104 g) ÷ (4 x 101 cm3 )
2 x 103 g/cm3
41
Slide 42
Practice Problems: 33 ( 15-16)
16.Calculate the following densities. Report the
answers in g/cm3
c. (9 x 105 g) ÷ (3 x 10-1 cm3 )
3 x 106 g/cm3
d. (4 x 10-3 g) ÷ (2 x 10-2 cm3 )
2 x 10-1 g/cm3
42
Slide 43
Practice Problems: 34 (17-18)
17.
a. Convert 360 s to ms
1s = 1000ms
360s 1000 ms = 360000 ms
1s
= 3.6 x 105 ms
43
Slide 44
Practice Problems: 34 (17-18)
17.
b. Convert 4800 g to kg
1kg = 1000g
4800g 1 kg
= 4.8 kg
1000g
44
Slide 45
Your Turn
17.
c. Convert 5600 dm to m
d. Convert 72 g to mg
45
Slide 46
Practice Problems: 34 (17-18)
18.
a. Convert 245 ms to s
b. Convert 5 m to cm
c. Convert 6800 cm to m
d. Convert 25 kg to Mg
46
Slide 47
Practice Problems: 34 (17-18)
18.
a. Convert 245 ms to s
1s = 1000ms
245 ms 1s
1000 ms
= 0.245 s
47
Slide 48
Practice Problems: 34 (17-18)
18.
b. Convert 5 m to cm
1m= 100 Cs
5m
100 cm
1m
= 500 cm
48
Slide 49
Your Turn...
18.
c. Convert 6800 cm to m
d. Convert 25 kg to Mg
49
Slide 50
Practice Problems: 35(19-21)
19.How many seconds are there in 24 hours?
20.The density of gold is 19.3 g/mL. What is
gold’s density in decigrams per liter?
21. a car is traveling 90.0 kilometers per hour.
What is its speed in miles per minute? One
kilometer = 0.62 miles.
50
Slide 51
Practice Problems: 35(19-21)
19.
a. How many seconds are there in 24 hours?
24 hrs
60 min 60 sec
1hr
1min
= 86,400 sec
51
Slide 52
Practice Problems: 35(19-21)
20. The density of gold is 19.3 g/mL. What is
gold’s density in decigrams per liter?
19.3 g
mL
1000mL 10 dg
1L
1g
= 193,000 dg/L
52
Slide 53
Your Turn...
21. a car is traveling 90.0 kilometers per hour.
What is its speed in miles per minute? One
kilometer = 0.62 miles.
53
Section 2.2
1
Slide 2
Section 2.2 Scientific Notation and Dimensional Analysis
Section 2-2
• Express numbers in scientific notation.
• Convert between units using dimensional analysis.
quantitative data: numerical information describing
how much, how little, how big, how tall, how fast, and
so on
Slide 3
Section 2.2 Scientific Notation and Dimensional Analysis (cont.)
Section 2-2
scientific notation
dimensional analysis
conversion factor
Scientists often express numbers in scientific
notation and solve problems using
dimensional analysis.
Slide 4
Scientific Notation and Dimensional Analysis
Standard I&E: 1e
Terms: 31
Mastering Concepts: 50 (58-61)
Practice Problems: 32(12-14),33(15-16)34(17),35(1921)
Homework:
Cornell Notes: 2.2
Section Assessment: 35(22-26)
Mastering Problems: 50 (75-80)
10 Stamps
4
Slide 5
Metric System
Prefixes convert the base units into units that are
appropriate for the item being measured.
5
Slide 6
SI Units
• Système International d’Unités
• Uses a different base unit for each quantity
6
Slide 7
Scientific Notation
Section 2-2
• Scientific notation can be used to express
any number as a number between 1 and 10
(the coefficient) multiplied by 10 raised to a
power (the exponent).
• Count the number of places the decimal
point must be moved to give a coefficient
between 1 and 10.
Slide 8
Scientific Notation (cont.)
Section 2-2
• The number of places moved equals the
value of the exponent.
• The exponent is positive when the
decimal moves to the left and negative
when the decimal moves to the right.
800 = 8.0 102
0.0000343 = 3.43 10–5
Slide 9
Scientific Notation (cont.)
Section 2-2
• Addition and subtraction
– Exponents must be the same.
– Rewrite values with the same
exponent.
– Add or subtract coefficients.
Slide 10
Scientific Notation (cont.)
Section 2-2
• Multiplication and division
– To multiply, multiply the coefficients, then add the
exponents.
– To divide, divide the coefficients, then subtract the
exponent of the divisor from the exponent of the
dividend.
Slide 11
Dimensional Analysis
Section 2-2
• Dimensional analysis is a systematic
approach to problem solving that uses
conversion factors to move, or convert,
from one unit to another.
• A conversion factor is a ratio of equivalent
values having different units.
Slide 12
Dimensional Analysis (cont.)
Section 2-2
• Writing conversion factors
– Conversion factors are derived from
equality relationships, such as 1
dozen eggs = 12 eggs.
– Percentages can also be used as
conversion factors. They relate the
number of parts of one component
to 100 total parts.
Slide 13
Dimensional Analysis (cont.)
Section 2-2
• Using conversion factors
– A conversion factor must cancel one unit and
introduce a new one.
Slide 14
Sec. 2.2 Cornell Notes
Summary
Scientists often
express numbers in
scientific notation and
solve problems using
dimensional analysis.
2.2 Scientific Notation and Dimensional
Analysis
• Scientific notation makes it easier to handle
extremely large or small measurements.
• Numbers expressed in scientific notation are
a prod- uct of two factors: (1) a number
between 1 and 10 and (2) ten raised to a
power.
• Numbers added or subtracted in scientific
notation must be expressed to the same
power of ten.
• When measurements are multiplied or
divided in scientific notation, their exponents
are added or subtracted, respectively.
• Dimensional analysis often uses conversion
factors to solve problems that involve units.14A
Slide 15
Standard: I&E
1.e Solve scientific problems by using
quadratic equations and simple
trigonometric, exponential, and
logarithmic functions.
Vocabulary
scientific notation
conversion factor
dimensional analysis
15
Slide 16
Mastering Concepts: 50 (58-61)
Slide 17
Mastering Concepts: 50 (58-61)
58. How does scientific notation differ from ordinary
notation? (2.2)
Scientific notation uses a number between 1 and 10
times a power of ten to indicate the size of very large
or small numbers.
59. If you move the decimal place to the left to convert
a number into scientific notation, will the power of ten
be positive or negative? (2.2)
positive
60. When dividing numbers in scientific notation, what
must you do with the exponents? (2.2)
Subtract them.
61. When you convert from a small unit to a large unit,
what happens to the number of units? (2.2)
17
It decreases.
Slide 18
Significant Figures:
Rules for counting significant figures
All nonzero numbers count
Leading zeros don’t count
Trailing zeros count if there is a decimal
Trailing zeros don’t count if there is no decimal
18
Slide 19
Practice Problems: 32(12-13)
12.Express the following quantities in scientific
notations:
a) 700 m
b) 38 000m
c) 4 500 000 m
d) 685 000 000 000 m
e) 0.0054 kg
f) 0.000 006 87 kg
g) 0.000 000 076 kg
h) 0.000 000 000 8 kg
19
Slide 20
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
a. 700 m
700.
= 7 X 102 m
20
Slide 21
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
b. 38 000 m
38000.
3.8 X 104 m
21
Slide 22
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
c. 4 500 000 m
4 500000
4.5 X 106 m
22
Slide 23
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
d. 685 000 000 000 m
685000000000
6.85 X 1011 m
23
Slide 24
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
e. 0.0054 kg
0.0054
5.4 X 10-3 kg
24
Slide 25
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
f. 0.000 006 87 kg
0.000 006 87
6.87 X 10-6 kg
25
Slide 26
Your Turn
12.
Express the following quantities in scientific
notation. Move decimal until one number to
the left.
g. 0.000 000 076 kg
h. 0.000 000 000 8 kg
26
Slide 27
Practice Problems: 32(12-13)
13. Express the following quantities in scientific
notations:
a.
b.
c.
d.
360 000 s
0.000 054 s
5060 s
89 000 000 000 s
27
Slide 28
13.
Express the following quantities in scientific
notation.
a. 360 000 s
360 000
3.6X105s
28
Slide 29
13.
Express the following quantities in scientific
notation.
b. 0.000 054 s
0.000 054
5.4 X10-5 s
29
Slide 30
Your Turn
13.
Express the following quantities in scientific
notation.
c. 5060 s
d. 89 000 000 000 s
30
Slide 31
Rules for calculating with significant figures:
• Addition and Subtraction: You are only as
good as your least accurate place value
31
Slide 32
Practice Problems: 32 (14)
Solve the following addition and subtraction problems.
Express your answers in scientific notation.
a. 5 x 10 -5 m + 2 x 10-5 m
b. 7 x 10 8 m - 4 x 10 8 m
c. 9 x 10 2 m - 7 x 10 2 m
d. 4 x 10 -12 m + 1 x 10 -12 m
e. 1.6 x 104 kg + 2.5 x 103 kg
f. 7.06 x 10-3 kg + 1.2 x 10-4 kg
g. 4.39 x 105 kg - 2.8 x 104 kg
h. 5.36 x 10-1 kg – 7.40 x 10-2 kg
32
Slide 33
Practice Problems: 32 (14)
Solve the following addition and subtraction
problems. Express your answers in scientific
notation.
a. 5 x 10 -5 m + 2 x 10-5 m =
7x10-5 m
b. 7 x 10 8 m - 4 x 10 8 m=
3x108m
33
Slide 34
Practice Problems: 32 (14)
Solve the following addition and subtraction
problems. Express your answers in scientific
notation.
c. 9 x 10 2 m - 7 x 10 2 m=
2x102m
d. 4 x 10 -12 m + 1 x 10 -12 m=
5x10-12 m
34
Slide 35
e. 1.6 x 104 kg + 2.5 x 103 kg=
1.6 x 104 kg + 0.25 x 104 kg=
1.85x104 m
f. 7.06 x 10-3 kg + 1.2 x 10-4 kg=
7.06 x 10-3 kg + 0.12 x 10-3 kg=
7.18 x 10-3 kg
35
Slide 36
g. 4.39 x 105 kg - 2.8 x 104 kg=
4.39 x 105 kg – 0.28 x 105 kg=
4.11 x 105 kg
h. 5.36 x 10-1 kg – 7.40 x 10-2 kg=
5.36 x 10-1 kg – 0.740 x 10-1 kg=
4.62 x 10-1 kg
36
Slide 37
Rules for calculating with significant figures:
• Multiplication and Division: You are only as
good as your least accurate number of
significant figures
37
Slide 38
Practice Problems: 33 ( 15-16)
15. Calculate the following areas. Report the
answers in square centimeters, cm2
a. (4 x 102 cm ) X (1 x 108 cm)
b. (2 x 10-4 cm ) X (3 x 102 cm)
c. (3 x 101 cm ) X (3 x 10-2 cm)
d. (1 x 103 cm ) X (5 x 10-1 cm)
38
Slide 39
Practice Problems: 33 ( 15-16)
15. Calculate the following areas. Report the
answers in square centimeters, cm2
a. (4 x 102 cm ) X (1 x 108 cm)
4 x 1010 cm2
b. (2 x 10-4 cm ) X (3 x 102 cm)
6 x 10-2 cm2
39
Slide 40
Practice Problems: 33 ( 15-16)
15.Calculate the following areas. Report the
answers in square centimeters, cm2
c. (3 x 101 cm ) X (3 x 10-2 cm)
9 x 10-1 cm2)
d. (1 x 103 cm ) X (5 x 10-1 cm)
5 x 102 cm2
40
Slide 41
Practice Problems: 33 ( 15-16)
16. Calculate the following densities. Report the
answers in g/cm3
a. (6 x 102 g) ÷ (2x 101 cm3 )=
3 x 101 g/cm3
b. (8 x 104 g) ÷ (4 x 101 cm3 )
2 x 103 g/cm3
41
Slide 42
Practice Problems: 33 ( 15-16)
16.Calculate the following densities. Report the
answers in g/cm3
c. (9 x 105 g) ÷ (3 x 10-1 cm3 )
3 x 106 g/cm3
d. (4 x 10-3 g) ÷ (2 x 10-2 cm3 )
2 x 10-1 g/cm3
42
Slide 43
Practice Problems: 34 (17-18)
17.
a. Convert 360 s to ms
1s = 1000ms
360s 1000 ms = 360000 ms
1s
= 3.6 x 105 ms
43
Slide 44
Practice Problems: 34 (17-18)
17.
b. Convert 4800 g to kg
1kg = 1000g
4800g 1 kg
= 4.8 kg
1000g
44
Slide 45
Your Turn
17.
c. Convert 5600 dm to m
d. Convert 72 g to mg
45
Slide 46
Practice Problems: 34 (17-18)
18.
a. Convert 245 ms to s
b. Convert 5 m to cm
c. Convert 6800 cm to m
d. Convert 25 kg to Mg
46
Slide 47
Practice Problems: 34 (17-18)
18.
a. Convert 245 ms to s
1s = 1000ms
245 ms 1s
1000 ms
= 0.245 s
47
Slide 48
Practice Problems: 34 (17-18)
18.
b. Convert 5 m to cm
1m= 100 Cs
5m
100 cm
1m
= 500 cm
48
Slide 49
Your Turn...
18.
c. Convert 6800 cm to m
d. Convert 25 kg to Mg
49
Slide 50
Practice Problems: 35(19-21)
19.How many seconds are there in 24 hours?
20.The density of gold is 19.3 g/mL. What is
gold’s density in decigrams per liter?
21. a car is traveling 90.0 kilometers per hour.
What is its speed in miles per minute? One
kilometer = 0.62 miles.
50
Slide 51
Practice Problems: 35(19-21)
19.
a. How many seconds are there in 24 hours?
24 hrs
60 min 60 sec
1hr
1min
= 86,400 sec
51
Slide 52
Practice Problems: 35(19-21)
20. The density of gold is 19.3 g/mL. What is
gold’s density in decigrams per liter?
19.3 g
mL
1000mL 10 dg
1L
1g
= 193,000 dg/L
52
Slide 53
Your Turn...
21. a car is traveling 90.0 kilometers per hour.
What is its speed in miles per minute? One
kilometer = 0.62 miles.
53