1. Section 2.2

2. Section 2-2 Express numbers in scientific notation.
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

3. Section 2-2 scientific notation dimensional analysis conversion factor
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.

4. Scientific Notation and Dimensional Analysis
Standard I&E: 1e Terms: Mastering Concepts: 50 (58-61) Practice Problems: 32(12-14),33(15-16)34(17),35(19- 21)
Homework:
Cornell Notes: 2.2
Section Assessment: 35(22-26)
Mastering Problems: 50 (75-80) Stamps

5. Metric System
Prefixes convert the base units into units that are appropriate for the item being measured.

6. SI Units Système International d’Unités
Uses a different base unit for each quantity

7. Section 2-2
Scientific Notation
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.

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
= 3.43  10–5

9. Section 2-2 Addition and subtraction Exponents must be the same.
Scientific Notation (cont.)
Section 2-2
Addition and subtraction
Exponents must be the same.
Rewrite values with the same exponent.
Add or subtract coefficients.

10. Section 2-2 Multiplication and division
Scientific Notation (cont.)
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.

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.

12. Section 2-2 Writing conversion factors
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.

13. Section 2-2 Using conversion factors
Dimensional Analysis (cont.)
Section 2-2
Using conversion factors
A conversion factor must cancel one unit and introduce a new one.

14. Sec. 2.2 Cornell Notes
Summary 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. A conversion factor is a ratio of equivalent values.
Scientists often express numbers in scientific notation and solve problems using dimensional analysis.

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

16. Mastering Concepts: 50 (58-61)

17. 58. How does scientific notation differ from ordinary notation? (2.2)
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)
It decreases.

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

19. Practice Problems: 32(12-13)
Express the following quantities in scientific notations:
a) 700 m
b) m
c) m
d) m
e) kg
f) kg
g) kg
h) kg

20. 12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
700 m
700.
= 7 X 102 m

21. 12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
b m 
38000.
3.8 X 104 m

22. 12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
c m 
4.5 X 106 m

23. 12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
d m 
6.85 X 1011 m

24. 12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
e kg 
0.0054
5.4 X 10-3 kg

25. 12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
f kg 
6.87 X 10-6 kg

26. Your Turn
12.
Express the following quantities in scientific notation. Move decimal until one number to the left.
g kg
h kg

27. Practice Problems: 32(12-13)
13. Express the following quantities in scientific notations: s s
5060 s s

28. 360 000 13. Express the following quantities in scientific notation.
3.6X105s

29. 0.000 054 13. Express the following quantities in scientific notation.
b s 
5.4 X10-5 s

30. Your Turn 13. Express the following quantities in scientific notation.
c s
d s

31. Rules for calculating with significant figures:
Addition and Subtraction: You are only as good as your least accurate place value

32. Practice Problems: 32 (14)
Solve the following addition and subtraction problems. Express your answers in scientific notation.
5 x m + 2 x 10-5 m
7 x 10 8 m - 4 x 10 8 m
9 x 10 2 m - 7 x 10 2 m
4 x m + 1 x m
1.6 x 104 kg x 103 kg
7.06 x 10-3 kg x 10-4 kg
4.39 x 105 kg x 104 kg
5.36 x 10-1 kg – 7.40 x 10-2 kg

33. Practice Problems: 32 (14)
Solve the following addition and subtraction problems. Express your answers in scientific notation.
5 x m + 2 x 10-5 m =
7x10-5 m
b. 7 x 10 8 m - 4 x 10 8 m=
3x108m

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 m + 1 x m=
5x10-12 m

35. e. 1.6 x 104 kg x 103 kg=
1.6 x 104 kg x 104 kg=
1.85x104 m
f x 10-3 kg x 10-4 kg=
7.06 x 10-3 kg x 10-3 kg=
7.18 x 10-3 kg

36. g x 105 kg x 104 kg=
4.39 x 105 kg – 0.28 x 105 kg=
4.11 x 105 kg
h x 10-1 kg – 7.40 x 10-2 kg=
5.36 x 10-1 kg – x 10-1 kg=
4.62 x 10-1 kg

37. Rules for calculating with significant figures:
Multiplication and Division: You are only as good as your least accurate number of significant figures

38. Practice Problems: 33 ( 15-16)
15. Calculate the following areas. Report the answers in square centimeters, cm2
(4 x 102 cm ) X (1 x 108 cm)
(2 x 10-4 cm ) X (3 x 102 cm)
(3 x 101 cm ) X (3 x 10-2 cm)
(1 x 103 cm ) X (5 x 10-1 cm)

39. Practice Problems: 33 ( 15-16)
15. Calculate the following areas. Report the answers in square centimeters, cm2
(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

40. Practice Problems: 33 ( 15-16)
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

41. Practice Problems: 33 ( 15-16)
16. Calculate the following densities. Report the answers in g/cm3
(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

42. Practice Problems: 33 ( 15-16)
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

43. Practice Problems: 34 (17-18)
17.
Convert 360 s to ms
1s = 1000ms
360s ms = ms 1s
= 3.6 x 105 ms

44. Practice Problems: 34 (17-18)
17.
b. Convert 4800 g to kg
1kg = 1000g
4800g 1 kg = 4.8 kg
1000g

45. Your Turn
17.
c. Convert 5600 dm to m
d. Convert 72 g to mg

46. Practice Problems: 34 (17-18)
18.
Convert 245 ms to s
Convert 5 m to cm
Convert 6800 cm to m
Convert 25 kg to Mg

47. Practice Problems: 34 (17-18)
18.
Convert 245 ms to s
1s = 1000ms
245 ms 1s
1000 ms
= s

48. Practice Problems: 34 (17-18)
18.
b. Convert 5 m to cm
1m= 100 Cs
5 m cm 1m
= 500 cm

49. Your Turn...
18.
c. Convert 6800 cm to m
d. Convert 25 kg to Mg

50. Practice Problems: 35(19-21)
How many seconds are there in 24 hours?
The density of gold is 19.3 g/mL. What is gold’s density in decigrams per liter?
a car is traveling 90.0 kilometers per hour. What is its speed in miles per minute? One kilometer = 0.62 miles.

51. Practice Problems: 35(19-21)
19.
a. How many seconds are there in 24 hours?
24 hrs min sec
1hr min
= 86,400 sec

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 dg
mL L g
= 193,000 dg/L

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.