CHAPTER 2. SCIENTIFIC MEASUREMENTS Problems to Practice in the text book. Answers are in Appendix I. # 1, 3, 5, 9, 11, 13, 15, 17, 19, 21, 23, 25, 31, 33, 35, 37, 39, 41, 45, 49, 55, 57, 59, 61, 63, 65, 67, 69, 73, 75, 79, 81, 83, 85, 89, 91, 93

2.1 Uncertainty in Measurements Measurement – number with a unit, all measurements have uncertainty. An instrument must be used to obtain a measurement, so some error or uncertainty is involved. E.g. A ruler measurement, weight obtained from a scale. 

All measurements have some uncertainty involved since instrument used can never give exact measurements!

Length: measures distance, units are meters (m, cm, mm, km…) Mass: measure of the amount of matter an object possesses; mass is not affected by gravity. Mass is usually reported in grams or kilograms Weight: a measure of the force of gravity. Mass is same anywhere, but weight may differ. E.g. An astronaut may weigh 170 lbs on earth, but only 29 lbs on the moon. Mass is measured using a balance. Volume: amount of space occupied by a substance. Volume is measured using beakers, graduated cylinders, burets and pipets. 3

Volume units are usually liters (L), milliliters (mL), or cubic centimeters (cm ) 3

1 mL = 1 cm = 1 cc You should know the following English volume relationships: 1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

2.2 Significant Digits also called Significant Figures or “Sig figs” Significant Figures: All digits in a measurement that are known plus 1st uncertain or estimated digit - this is the doubtful digit. Ex: Recording a ruler measurement (see Figure 2.2) Guidelines for Counting Significant Figures 1. Numbers 1-9 are always significant. 185.27 has 5 sig figs 2. Zeroes in front are never significant. 0.00001234 has 4 sig figs 3. Zeroes at the end of a number AND after a decimal point are significant. 6.7000 has 5 sig figs, 0.00270 has 3 4. Zeroes between significant digits count. 0.00409 has 3 sig figs, 2850,034 has 7 sig figs Note that significant figure rules do not apply for exact numbers! Exact numbers have infinite sig figs. Exact number: counted or defined numbers – no uncertainty involved, not a measurement. E.g. 34 students in a class, 12 eggs in a dozen; 12 inches per foot, 1 km per 1000 m

2.3 Rounding Off Nonsignificant Digits Rules for rounding numbers: 1. < 5, don’t round up 2. ≥ 5, round up 3. Don't change the magnitude of the number – use placeholder zeroes Example. Round these numbers off to 3 significant figures. 1) 1.42752 = 1.43

2) 6432.3 = 6430 NOT 643

3) 22.75 = 22.8

2.4 Adding and Subtracting Measurements Addition and subtraction: Your final answer is limited by the number with the fewest decimal places. Round off your final answer based on the number with the fewest decimal places. GCC CHM130

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Example.

20.4 - 1.3222 19.0778

Final answer = 19.1

Rounded to 19.1 since 20.4 has only one number after the decimal point

2.5 Multiplying and Dividing Measurements Multiplication and division: Your final answer is limited by the number with the least number of significant figures. Round off your final answer based on the number with the fewest significant figures. Example. 6.221 cm

5.2 cm = 32 cm

2

(Note: 32.3492 is rounded to 2 sig figs since 5.2 has 2 sig figs)

2.6 and 2.7 Exponential Numbers and Scientific Notation Convenient method for expressing very large or very small numbers. + exponent means number is > 1; - exponent means number is < 1 1

2

-1

-3

4

Examples: 10 = 10 , 10 = 100, 10 = 0.1, 10 = 0.001, 10 = 10,000 Two Parts to Writing Numbers in Scientific Notation: 1) a digit - this is a number between 1 and 10  Obtain by expressing number with one digit followed by a decimal point. 2) an exponential term that is 10 raised to a power 

Value of exponent is obtained by counting the number of places that the point must be moved to give one digit followed by a decimal point.



For big #’s > 1, move the decimal point to the left



For small #’s < 1, move the decimal point to the right

positive exponent negative exponent.

Example. Convert the following to scientific notation: 1) 100.03 = 1.0003

2

10

2) 0.000340 = 3.40

-4

10

-4

In your calculator punch in 3.40 x 10 as 3.40 EE – 4. The “EE” button literally means “times ten to the power of” Do not punch in x 10 ^ - 4. That is wrong. Use your EE button. (Some calculators call it the EXP button) Use it!!! Note you may not use graphing or programmable calculators or your cell phones on quizzes or exams. Buy a proper scientific calculator for class please.

2.8 Unit Equation and Unit Factor Unit equation is a statement of two equivalent quantities: Examples. 10 dimes = 1 dollar; 60 s = 1 min Unit factor is a fraction conversion factor, a ratio of 2 equivalent quantities and can be written two ways: Examples.

1dollar 10 dim es or 1 dollar 10 dim es

;

60 s 1 min or 1 min 60 s

2.9 Unit Analysis Problem Solving We will use this method for problem solving throughout the semester! PROCEDURE 1. Identify units for what you want to FIND (answer). 2. Identify the GIVEN (starting point). 3. Multiply GIVEN quantity by 1 or more unit factors (shown as fractions) so that all units cancel except the units needed for the final answer. (Include units in your set-up!) 4. Check for correct units and round the final answer to the proper number of sig figs. When performing conversions, SHOW ALL WORK for full points in this class! If your set-up is correct, then all units cancel except for desired units. GCC CHM130

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Note that exact conversion factors and exact counted values do not limit sig figs. Use sig fig rules only for measured values (e.g. 15.8 g) or inexact equivalents (e.g. 1.61 km = 1 mile).

2.10 The Percent Concept Percent: Ratio of parts per 100 parts. (e.g. 80% is To calculate Percent: percent =

# of parts whole sample

80 ) 100 100%

Note: Both the “part” and the “whole” must be expressed in the same unit. The percentage may be used to solve problems as a conversion factor.

CHAPTER 2 PRACTICE PROBLEMS Example 1. You just won 685 nickel playing nickel slots. How many dollars is this? GIVEN: 685 Nickels

Wanted: ? dollars

Unit Factors: 20 nickels = 1 dollar

1 dollar 685 Nickels ( 20 nickels ) = $ 34.25 Example 2. How many seconds are in an 8 hour work day? GIVEN: 8 Hrs 8 hrs (

WANTED: ? sec

Unit Factors: 1 hour = 60 min; 1 min = 60 s

60 min 60 sec 1 hr )( 1 min ) = 28,800 sec

Example 3: A sample of coal is 3.2% sulfur by mass. a) Write two conversion factors using this information (3.2 g sulfur / 100 g coal)

or

(100 g coal / 3.2 g sulfur)

b) How many grams of sulfur are contained in a 35 gram sample of this coal?

35 g coal 3.2 g sulfur 1 100 g coal = 1.1 g sulfur c) Burning coal produces air pollutants, such as sulfur dioxide, that can lead to acid rain. How many grams of coal are burned in the production of 8.75 g of toxic sulfur?

8.75 g sulfur 1

100 g coal 3.2 g sulfur

2

= 2.7x10 g coal

1. Determine the number of significant figures in each of the following. a. 0.00036

___

b. 0.140150

___

c. 39.00

___

d. 670

___

2. Round the following to the number of significant figures indicated: a. Round 56,028 to 2 sig figs GCC CHM130

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b. Round 0.00062187 to 3 sig figs c. Round 2.00039 to 4 sig figs 3. Perform the following operations, expressing each answer to the correct number of significant figures. a. 862 + 14.71 + 1.1 = b. 725.50 ￚ 103 = 5.60 c. 2.800 = d. (6.43 e. 1.90

-7

10 ) x (4.5 15

10 )

(2.500

8

10 ) = 8

10 ) =

4. Express these numbers in exponential notation. a. 0.000823 b. 135,200 c. 8.714 d. 0.00000002710 5. You just won 1460 quarters playing quarter slots. How many dollars is this?

6. You decide to take a trip to San Diego, which is about 355 miles from Glendale. If you average 65 mph with no stops, how many hours does it take to get there?

7. Convert 55.8

m ile km to . (1 mile = 1.61 km) s hr

8. How many yards are there in a 26.2 mile marathon? (There are 5280 feet in one mile and 3 feet in one yard)

9. If 12.5 gallons of gasohol contains 1.50 gal of ethyl alcohol, what is the percent of alcohol in the gasoline? GCC CHM130

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10. Air is 20.9% oxygen by volume. Find the volume of air that contains 225 mL of oxygen.

11. A dancer who weighs 125 lbs has 18.0 % body fat by weight. How many lbs of body fat does her body contain?

Answers to Practice Problems 1. a. 2

b. 6

c. 4

2. a. 56,000

b. 0.000622

3. a. 878

b. 623

4. a. 8.23 x 10

-4

1460 quarters

6.

355 miles

7.

55.8 miles hr

9.

c. 2.000

c. 2.00

b. 1.352 x 10

5.

8. 26.2 miles

d. 2

2

d. 2.9 x 10

5

e. 7.60 x 10 0

c. 8.714 x 10

6

d. 2.710 x 10

-8

1 dollar = $365 4 quarters

1 hr = 5.5 hours 65 miles

1.61 km 1 mile 5280 ft 1 mile

1hr 60 min

1 yd 3 ft

1 min km = 0.0250 60 s s

= 4.61x104 yd

1.50 gal alcohol x 100% = 12.0 % alcohol 12.5 gal gasohol

10.

225 mL oxygen

11.

125 lbs

GCC CHM130

100 mL air = 1080 mL air 20.9 mL oxygen

18.0 lbs body fat 100lbs

= 22.5 lbs

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