Math for Liberal Arts MAT 110 : Chapter 2 Notes David J. Gisch A - - PowerPoint PPT Presentation

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Math for Liberal Arts MAT 110 : Chapter 2 Notes

David J. Gisch

A Quick Fractions Review

• Adding & Subtracting

A Quick Fractions Review

• Multiplying and Dividing

Percents and Decimals

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The Problem-Solving Power of Units

S ection 2A: The Problem-S

• lving Power of Units
• What are some common unit labels?

S ection 2A: The Problem-S

• lving Power of Units

The units of a quantity describe what is being measured or counted.

Read kilowatts  hours as “kilowatt-hours.” hyphen Multiplication Read ft  ft  ft, or ft3, as “cubic feet” or “feet cubed.” cube or cubic Raising to third power Read ft  ft, or ft2, as “square feet” or “feet squared.” square Raising to second power Read miles  hours as “miles per hour.” per Division Exam ple Key word or sym bol Operation

Conversion Factors

A conversion factor is a statement of equality that is used to convert between units. Give me some examples.

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Equivalent Forms of Conversion Factors

Unit Conversions

• Use the form of the conversion factor that

allows you to cancel labels. Example 2.A.1: Convert each of the following. (a) 8 in. to feet. (b)55 inches to meters

A Chain of Conversions

Conversions of Units Raised to Powers

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Example 2.A.2: What is the conversion factor for cubic feet and cubic inches?

Conversions of Units Raised to Powers

Example 2.A.3: Convert 9 to cubic inches.

Conversions of Units Raised to Powers

Example 2.A.4:If

21.2 blahs = 4.1 ohhs

Convert 20 ohhs to blahs.

Currency Conversion

$1.41 = 1₤ 99.34 yen = $1

Example 2.A.5: If you return from Europe with 145 euros, how many dollars do you have?

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S tandardized Units: More Problem-S

• lving Power

S tandardized Unit S ystems

The International Metric System (or SI)

▫ Wide international use

U.S. Custom ary System (USCS) (or English system)

▫ Used in the United States

U.S . Customary S ystem

• Units of length were based on individual body

measurements.

▫ A foot was once the length of the measurer’s foot. ▫ An inch was the thumb-width of the measurer. ▫ A mile was one thousand paces.

• There are three distinct sets of units used to

measure weight.

1. Jewelers used troy measures of weight. 2. Pharmacists used apothecary measures of weight. 3. Other commerce was conducted with avoirdupois measures of weight.

• The basic unit of volume is the cubic inch (in.3).

▫

Dry and liquid measures differ.

U.S . Customary S ystem

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International Metric S ystem

• The metric system was designed to

1. replace many customary units with a few basic units.

• 2. simplify conversions through the use of a

decimal (base 10) system.

• The following are basic metric units:

▫

m eter (m) for length

▫

gram (g) for mass

▫

second (s) for time

▫

liter (L) for volume

Metric Conversions

Moving between metric units requires shifting the decimal place

• ne to the right when going to the next sm aller unit and one to the

left when going to the next larger unit. (Example: 5.23 cm = 52.3 mm)

Metric Conversions

10,000 mm = ? Hm 10 KL = ? dL

Metric-US CS Conversions

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Metric-US CS Conversions

Example 2.B.1:What is the conversion factor for square yards and square meter?

Metric-US CS Conversions

Example 2.B.2: In track and field, the 1600 meter race is often referred to as the mile. Are these terms really the same?

Physics Conversions

Example 2.B.3: Convert 30 to meters per second.

Temperature Units

Three temperature scales are commonly used today. A temperature of 0 is the coldest possible temperature, known as absolute zero.

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Units of Energy and Power

• Energy is what makes matter move or heat up.

▫ International metric unit is the joule

• Power is the rate at which energy is used.

▫ International metric unit is the watt 1 watt 1 j s

• A kilowatt-hour is a unit of energy.

1 3.6

Operating cost of a Light Bulb

Example 2.B.4: A utility company charges 12.5¢ per kilowatt-hour of electricity. How much does it cost to keep a 75-watt light bulb on for a week?

Units of Density and Concentration

Density describes compactness or crowding

• Material density is given in units of mass per

unit volume.

▫ e.g., grams per cubic centimeter ( ⁄ )

• Population density is given by the number of

people per unit area.

▫ e.g., people per square mile ( ⁄ )

• Inform ation density is given in units of mass per

unit volume.

▫ e.g., gigabytes per square inch ( ⁄ )

Units of Density and Concentration

Concentration describes the amount of one substance mixed with another.

• The concentration of an air pollutant is often

measured by the number of molecules of the pollutant per million molecules of air.

▫ e.g., parts per m illion (ppm )

• Blood alcohol content (BAC) describes the

concentration of alcohol in a person’s body.

▫ e.g., gram s of alcohol per 100 m illiliters of blood

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Population Density

Example 2.B.5: The land area of the United States is about 3.5 million square miles, and the population is about 300 million people. What is the average population density?

Problem-S

• lving Guidelines and Hints

Four S tep Problem-S

• lving Process

Step 1: Understand the problem. Step 2: Devise a strategy for solving the problem. Step 3: Carry out your strategy, and revise if necessary. Step 4: Look back to check, interpret, and explain your result.

Problem S

• lving

Example 2.C.1: Find the total number of possible squares on the chessboard.

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Ticket S ales

Example 2.C.2: A school is putting on a play and they are selling tickets at a cost of $8 for adults and $5 for students. If they sold $68 worth of tickets, how many of each kind did they sell?

A Condo

Example 2.C.3: You are going to buy a condo and have the choice of a deck or no deck, and granite, marble or quartz countertops. How many possible combinations are there?

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