Section 2.2

1

Section 2-2Section 2.2 Scientific Notation and Dimensional Analysis

• Express numbers in scientific notation.

quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on

• Convert between units using dimensional analysis.

Section 2-2Section 2.2 Scientific Notation and Dimensional Analysis (cont.)

scientific notationdimensional analysisconversion 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: 31 Mastering Concepts: 50 (58-61) Practice Problems: 32(12-14),33(15-16)34(17),35(19-21)

Homework:Cornell Notes: 2.2Section Assessment: 35(22-26) Mastering Problems: 50 (75-80) 10 Stamps

Metric SystemPrefixes convert the base units into units that are appropriate for the item being measured.

5

SI Units

• Système International d’Unités• Uses a different base unit for each quantity

6

Section 2-2Scientific 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.

Section 2-2Scientific Notation (cont.)

800 = 8.0 102

0.0000343 = 3.43 10–5

• 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.

Section 2-2Scientific Notation (cont.)

• Addition and subtraction

– Exponents must be the same.– Rewrite values with the same

exponent.– Add or subtract coefficients.

Section 2-2Scientific 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.

Section 2-2Dimensional Analysis

• 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.

Section 2-2Dimensional Analysis (cont.)

• 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.

Section 2-2Dimensional Analysis (cont.)

• Using conversion factors– A conversion factor must cancel one unit and

introduce a new one.

Summary2.2 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.

14

Scientists often express numbers in scientific notation and solve problems using dimensional analysis.

Sec. 2.2 Cornell Notes

15

1.e Solve scientific problems by using quadratic equations and simple trigonometric, exponential, and logarithmic functions.

Standard: I&E

Vocabularyscientific notation conversion factor dimensional analysis

Mastering Concepts: 50 (58-61)

17

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)positive60. 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.

Mastering Concepts: 50 (58-61)

Significant Figures:

Rules for counting significant figuresAll nonzero numbers countLeading zeros don’t countTrailing zeros count if there is a decimalTrailing zeros don’t count if there is no decimal

18

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

notations:a) 700 mb) 38 000mc) 4 500 000 md) 685 000 000 000 me) 0.0054 kgf) 0.000 006 87 kgg) 0.000 000 076 kgh) 0.000 000 000 8 kg

19

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

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

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

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

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

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

Your Turn

26

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

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

notations:

a. 360 000 sb. 0.000 054 sc. 5060 sd. 89 000 000 000 s

27

13.Express the following quantities in scientific notation.a. 360 000 s

360 000

3.6X105s28

13.Express the following quantities in scientific notation.b. 0.000 054 s

0.000 054 5.4 X10-5 s

29

13.Express the following quantities in scientific notation.c. 5060 s

d. 89 000 000 000 s

30

Your Turn

Rules for calculating with significant figures:

• Addition and Subtraction: You are only as good as your least accurate place value

31

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 mb. 7 x 10 8 m - 4 x 10 8 mc. 9 x 10 2 m - 7 x 10 2 md. 4 x 10 -12 m + 1 x 10 -12 me. 1.6 x 104 kg + 2.5 x 103 kgf. 7.06 x 10-3 kg + 1.2 x 10-4 kgg. 4.39 x 105 kg - 2.8 x 104 kgh. 5.36 x 10-1 kg – 7.40 x 10-2 kg

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 = 7x10-5 m

b. 7 x 10 8 m - 4 x 10 8 m= 3x108m

33

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

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

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

Rules for calculating with significant figures:

• Multiplication and Division: You are only as good as your least accurate number of significant figures

37

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

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

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

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

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

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

Practice Problems: 34 (17-18)17. b. Convert 4800 g to kg

1kg = 1000g

4800g 1 kg = 4.8 kg 1000g

44

17. c. Convert 5600 dm to md. Convert 72 g to mg

45

Your Turn

Practice Problems: 34 (17-18)

18. a. Convert 245 ms to sb. Convert 5 m to cmc. Convert 6800 cm to md. Convert 25 kg to Mg

46

Practice Problems: 34 (17-18)18. a. Convert 245 ms to s

1s = 1000ms

245 ms 1s 1000 ms

= 0.245 s

47

Practice Problems: 34 (17-18)18. b. Convert 5 m to cm

1m= 100 Cs

5 m 100 cm 1m

= 500 cm

48

18. c. Convert 6800 cm to m

d. Convert 25 kg to Mg

49

Your Turn...

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

19. a. How many seconds are there in 24 hours?

24 hrs 60 min 60 sec 1hr 1min

= 86,400 sec

51

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 1000mL 10 dg mL 1L 1g

= 193,000 dg/L

52

Practice Problems: 35(19-21)

21. a car is traveling 90.0 kilometers per hour. What is its speed in miles per minute? One kilometer = 0.62 miles.

53

Your Turn...