copyright © 2005 pearson education, inc. chapter 2

Copyright © 2005 Pearson Education, Inc.

Chapter 2

Copyright © 2008 Pearson Education, Inc. Slide 2-2

Units

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

Read kilowatts hours as “kilowatt-hours.”

hyphenMultiplication

Read ft ft ft or ft3, as

“cubic feet” or “feet cubed”

cube or cubicRaising to a third power

Read ft ft, or ft2, as

“square feet” or “feet squared”

squareRaising to a second power

Read miles hours as “miles per hour”

perDivision

ExampleKey word or symbol

Operation

2-A

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Solving Problems

Unit Conversions

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Using Units

Always keep units along with their quantities! Example

► 2500 watts x 3 hours = 7500 watt-hours► Not 2500 x 3 = 7500 watt-hours

Example► 1000 watt-hours = 1 kilowatt-hour► 500 watt-hours = 0.5 kilowatt-hour = 0.5 kw-hr

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Always keep units along with their quantities!

Why

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Keep Units with their Quantities!

Example: 12 ÷ 1 is not 1 But 12 inches ÷ 1 foot is 1, and 1 foot ÷ 12 inches is 1

because?

12 inches and 1 foot are equal!

12 Inches and 1 Foot are Equal


1 ft = 12 in

divide both sides by 12 in

1 ft 12 in = = 112 in 12 in

1 ft = 112 in

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Different Ways of Writing 1

mi 1

m 1609.3 or

km 1.6093

mi 1

in. 1

mm 25.4 or

cm 2.54

in. 1

2

2

2

2

in. 144

ft 1 or

ft 1

in. 144

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Conversions

Multiply, divide, or what? Simplify by multiplying by 1 Depends on what the problem is The key to solving the problem is knowing

what units the solution should be Example, if the answer should be

square yards (yd2), and your solution produces

yd4, then your solution is incorrect

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Using Units

Know the units to expect Examples

The question asks for a cost in $

when using conversions, all units, except for dollars, should cancel!

The question asks for speed in km/hr

when using conversions, all units, except for km/hr,

should cancel!

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Conversion Format

There are 12 inches per 1 foot:

Also, there is 1 foot per 12 inches:

Use whatever produces the desired units!

ft

in. 12 or

foot 1

inches 12

in. 12

ft or

inches 12

foot 1

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REPEAT!

Know the units to expect Examples

The question asks for a cost in $

when using conversions, all units, except for dollars,

should cancel! The question asks for speed in km/hr

when using conversions, all units, except for km/hr,

should cancel!


Unit Conversions

Convert a distance of 9 feet into inches.

2-A

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Chain of Conversions

If the problem doesn’t involve a simple conversion.such as “if you buy 2 pounds of apples when applesare 99 cents per pound, how much will you pay?”

Use a chain of units conversions, where each step involves multiplying by 1


Chain of Units Conversions

How many seconds are in one day?

2-A

24 hr 60 min 60 s

1 day 86,400 s1 day 1 hr 1 min


Using a Chain of Conversions

2-A


Conversions with Units Raised to Powers

1 yd2 = 1 yd × 1 yd

= 3 ft × 3 ft

= 9 ft2

2-A


Cubic Units

How many cubic yards of soil are needed to fill a planter that is 20 feet long by 3 feet wide by 4 feet tall?

The volume is 20 ft × 3 ft × 4 ft = 240 ft3

1 yd = 3 ft, so (1 yd)3 = (3 ft)3 = 27 ft3

2-A


Currency Conversions

2-A

You return from a trip to Europe with 120 euros. How many dollars do you have?


Problem Solving with Units

You are buying 50 acres of farm land at a cost of $12,500 per acre. What is the total cost?

The answer should be in dollars. We multiply acreage by the cost per acre:

2-A


U.S. Customary System

2-B



2-B


Metric Conversions

2-B

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 cm = 52.3 mm)


USCS-Metric Conversions

2-B

How many square miles are in 5 square kilometers?

1 km = 0.6214 mi, so (1 km)2 = (0.6214 mi)2 ≈ 0.3861 mi2

5 km2 ≈ 5 × 0.3861 mi2 ≈ 1.9305 mi2


Temperature Conversions

The conversions are given in both words and with formulas in which C, F, and K are Celsius, Fahrenheit, and Kelvin temperatures, respectively.

C = K 273.15Subtract 273.15Kelvin to Celsius

K = C + 273.15Add 273.15.Celsius to Kelvin

Subtract 32. Then divide by 1.8

Fahrenheit to Celsius

F = 1.8c + 32Multiply by 1.8. Then add 32.

Celsius to Fahrenheit

Conversion Formula

Conversion in Words

To Convert from

2-B


Units of Energy and Power

Energy – makes matter move or heat up; international metric unit is the joule

Power – the rate at which energy is used; international metric unit is the watt

Kilowatt-hour – unit of energy;

1 kilowatt-hour = 3.6 million joules

2-B


Operating Cost of a Light Bulb

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?

One watt = 1 joule/sec, so a 75 watt bulb uses 75 joules/sec. Find the number of joules used in a week:

2-B


Convert this result to kilowatt-hours:

2-B

Now find the total cost:


Units of Density and Concentration

Density describes compactness or crowding.

Material density – given in units of mass per unit volume; i.e., g/cm3

Population density – given by the number of people per unit area

Information density – how much information can be stored by digital media

2-B


Units of Density and Concentration

Concentration describes the amount of one substance mixed with another

Concentration of an air pollutant – measured by the number of molecules of the pollutant per million molecules of air.

Blood alcohol content – measured in units of grams of alcohol per 100 milliliters of blood.

2-B


Four Step Problem-Solving Process

2-C

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 Solving Guidelines and Hints

2-C

Hint 1: There may be more than one answer.

Hint 2: There may be more than one strategy.

Hint 3: Use appropriate tools.

Hint 4: Consider simpler, similar problems.

Hint 5: Consider equivalent problems with simpler solutions.

Hint 6: Approximations can be useful.

Hint 7: Try alternative patterns of thought.

Hint 8: Do not spin your wheels.

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Problem Solving Example

2-C

Find the total number of possible squares on the chessboard by looking for a pattern.

Solution:

Start with the largest possible square

There is only one wayto make an 8 x 8 square . . . .


Problem Solving Example

Find the total number ofpossible squares on thechessboard by looking for apattern.

Now, look for the number of ways to make a 7 x 7 square.

There are only four ways.


Problem Solving Example2-C

If you continue looking at 6 x 6, 5 x 5 squares, and so on, you will discover the perfect square pattern for this chessboard problem as indicated in the table on the next slide



Problem Solving Example2-C


n x n squares # 8 x 8 1 7 x 7 4 6 x 6 9 5 x 5 16 4 x 4 25 3 x 3 36 2 x 2 49 1 x 1 64

Total: 204

copyright © 2005 pearson education, inc. chapter 2

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