Section 2B

Standardized UnitsPages 101-112

2-B

Standardized Unit Systems

•Metric system (SI)– Système International

•U.S. customary system (USCS)– Roots from ancient Middle Eastern

civilizations

2-B

Unit conversions within systems.

Unit conversions between systems.

U.S. Customary System - Lengths

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page101

U.S. Customary System - Weights

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page102

U.S. Customary System - Volumes

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page102

Conversions within USCS

Ex1/103 In the Kentucky Derby, horses race 10 furlongs. How many miles is this?

18 mile

10 furlongs1 furlong

1.25 miles

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Conversions within USCS

Ex1/103 In 20,000 Leagues Under the Sea, does the title refer to an ocean depth?

3 .20000 60,000 .

1

6076.1 . 160000 .

1 . 5280

69046.6

naut milesleagues naut miles

league

ft milenaut miles

naut mile ft

miles

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[convert marine leagues to miles]

Conversions within USCS

51’/114 If 150 bushels of wheat are traded on one day, how many cubic inches are traded? how many cubic feet?

International Metric System

• Invented in France, late 18th century– Replace many customary units

with a few basic units– Simplify conversions by using a

base 10 system

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International Metric System

•The basic units are:– meter (m) for length– gram (g) for mass– second (s) for time– liter (L) for volume

2-B

Metric System - Prefixes

Moving between metric units requires shifting the decimal placeone to the right when going to the next smaller unit and one to theleft when going to the next larger unit.

(Example: 5.23 m)

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Conversions within Metric System

•Convert 19 decimeters to millimeters:– Move the decimal 2 places to the RIGHT:

– 1900 millimeters

•Convert 1378 g to kg:– Move the decimal 3 places to the LEFT:

– 1.378 kg

2-B

USCS - Metric  Conversions

USCS to Metric Metric to USCS

1 in. = 2.540 cm 1 cm = 0.3937 in.

1 ft = 0.3048 m  1 m = 3.28 ft

1 yd = 0.9144 m 1 m = 1.094 yd

1 mi = 1.6093 km 1 km = 0.6214 mi

1 lb = 0.4536 kg 1 kg = 2.205 lb

1 fl oz = 29.574 mL

1 mL = 0.03381 fl oz

1 qt = 0.9464 L 1 L = 1.057 qt

1 gal = 3.785 L 1 L = 0.2642 gal

2-B

Conversions between Metric and USCS

60*/114 Convert 1550 millimeters to yards.

63/114 Convert 45 liters to gallons.

65/114 Convert 8550 square feet to square meters.

67/114 Convert 10 kilograms per cubic meter to pounds per cubic foot.

More Practice103/117 You see oranges in an Italian

market priced at 0.8 euro per kilogram. What is the price in dollars per pound?

105/117 A French car manufacturer claims that its newest economy model has gas “mileage” of 20 kilometers per liter. What is the gas mileage in miles per gallon?

Homework

2B – Part I

Pages 113-117

#48,50,60,62,68,104,106

2-B

Temperature Units

•Fahrenheit (US)– Water freezes at 32ºF, boils at 212ºF

•Celsius (International)– Water freezes at 0ºC, boils at 100ºC

•Kelvin (Scientific)– Water freezes at 273.15K, boils at

373.15K– Coldest known temperature = 0 Kelvin(-459.67ºF = -273.15ºC)

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Converting Temperatures (page107)

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To Convert from Conversion Formula

Celsius to Fahrenheit   F = 1.8C + 32

Fahrenheit to Celsius C = (F-32)/1.8

Celsius to Kelvin K = C + 273.15

Kelvin to Celsius C = K - 273.15

Example

Ex6/108 A ‘normal’ human temperature is 98.6ºF What is that in Celsius and Kelvin?

F 32 98.6-32 66.6

C 371.8 1.8 1.8

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K C 273.15 37 273.15 310.15

98.6o F = 37o C = 310.15o K

Energy and Power• Energy is what makes matter move or heat

up. The international unit of energy is the joule.

• Power is the rate at which energy is used. The international metric unit of power is the watt, defined as

• A kilowatt-hour is a unit of energy and 1 kWh = 3600000 joules = 3.6 million joules

joule

1 watt 1second

2-B

1 kw x 1hr = 1000j/s x 60s/m x 60m/hr x 1 hr

93/116 Your refrigerator uses an average power of 350 watts, and your utility company charges 10 cents per kilowatt-hour of energy. How much does it cost to run your refrigerator for a year?

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Conversion:350 watts is 350 joules per second

Usage for one year:

Conversion from joules to kilowatt-hours (1 kilowatt-hour = 3.6 million joules):

Cost for one year:

Units of Density/Concentration

• Density (e.g. material, population) – describes compactness or crowding.– material: mass/volume (g/cm3)

– Population: people/mi2

• Concentration (e.g. pollutants, BAC) describes the amount of one substance mixed with another.– pollutants: ppm– BAC: g/100mL (legal limit is 0.08g/100mL)

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ExampleEx9/111-2 Manhattan Island has a

population of ≈ 1.5 million people living in an area of about 57 km2. What is its population density? How much space is available per person?

2

1,500,000people

57 km

people

densityarea

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2

people

km26,000

Example (for fun)Ex9/111-2(cont.) How much space is that per

person?

Which is roughly 6m×6m, or 20 ft × 20 ft

21km

26,000people

2-B

2

2

1km 1000m 1000m

26,000people 1km 1km

38m /person

ExampleEx10/112 An average-sized man has about

5L of blood, and an average 12-ounce beer contains 15g of alcohol. If all the alcohol were immediately absorbed into the bloodstream, what would his BAC be?

g

.003mL

15g alcohol

5000mL bloodconcentration

2-B

g g100mL 100 100mL.003 0.3

More Practice79/114 The land area of the US is about 3.5

million square miles, and the population is about 280 million people. What is the average population density?

83/114 A typical glass of wine contains about 20 grams of alcohol. Consider a 110-pound woman, with approximately 4 liters of blood who drinks two glasses of wine. Assuming immediate absorption, what is her BAC?

Homework

2B – Part II

Pages 113-117

#70, #72, #80, #84, #94

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