Standardized Units: More Problem Solving Power

2BStandardized Units:

More Problem Solving Power

In the beginning… ◦ 1 Foot was the length of the foot of the person that

was doing the measuring ◦ 1 inch = 1 thumb length (they found that 12 thumbs

were about 1 foot)◦ 1 mile = 1000 paces

This caused problems as the lengths varied from person to person.

The first permanent standardization began with King Henry I, he declared 1 yard = the length from his nose to the tip of his thumb on his outstretched arm.

US Customary System

Traditionally measuring weight had 3 distinct sets of units◦ Troy- jewelers◦ Apothecary – pharmacists◦ Avoirdupois – most other commerce

Avoirdupois is the only one that is still commonly used

Page 101-102- Tables 2.1, 2.2 and 2.3

Notice that liquid and dry measure units have the same names but are different sizes.

Conversion Tables

How many ounces is 115 pounds?

How many tons is 115 pounds?

Converting in USCS units

A boat is moving at 30 knots (nautical miles per hour). What is the speed in miles per hour?

Most soda cans contain 12 fluid ounces. How many cubic inches do they contain?

Converting in USCS Units

A small city produces 500,000 cubic feet of garbage per week. If all of this garbage were stacked neatly (in a nice vertical pile) on a 100-yard by 60 yard football field, how high would the pile be in feet?

Converting in USCS Units

103 = 10 x 10 x 10 = 1,000

10–3 = 1 = .00110 x 10 x 10

Powers of 10

Positive exponent- the number of zeros after the 1

100 = 1 102 = 100 1015 = 1 followed by 15 0’s

Negative exponent- the number of values to the right of the decimal

10-1 = .1 10-2 = .01 10-15 = the decimal followed by 14 zeros and then a 1

Powers of 10 Working with Exponents

Multiply- add the exponents 103 x 105 = 103 + 5 = 108

(10 10 10)(10 10 10 10 10) = 108 Divide- subtract the exponents

106 102 = 106 – 2 = 104

10 10 10 10 10 10 = 10 10 10 10 = 104 10 10

Powers of 10 Multiplying and Dividing

Powers of powers- multiply the exponents (103)2 = 106

(10 10 10)(10 10 10) = 106

Powers of 10 More Exponents

No shortcut, write them out and then add/subtract the values

◦ 102 + 104 = 100 + 10,000 = 10,100

◦ 105 – 103 = 100,000 – 1,000 = 99,000

Powers of 10Adding and Subtracting

Designed for 2 reasons◦ To replace many customary units with just a few

basic units◦ To simplify conversions by using the decimal

system

The International Metric System

Page 102

kilo hecto deca unit deci centi milli

When you move to the right, divide.When you move to the left, multiply.

Table 2.5

To convert in the metric system all we need to do is move the decimal over the appropriate number of spaces.

100 centimeters = 1 meter = .001 kilometers

5000 milligrams = 500 centigrams = 5 grams

The Metric System

Convert 2345 centigrams to grams

Convert 34.58 meters to kilometers

Convert 54.2 kiloliters to liters

Examples

State how much larger or smaller the first unit is from the second.

◦ millimeter, deciliter

◦ kilometer, micrometer

◦ cubic meter, cubic centimeter

Examples

Convert the following◦ Use Table 2.6, on page 106

105 centimeters to yards

150 pounds to kilograms

Metric-USCS Conversions

100 kilometers per hour to miles per hour

5.5 grams per cubic centimeter to pounds per cubic foot

25 miles per hour to kilometers per hour

Metric-USCS Conversions

Units ◦ Fahrenheit ◦ Celsius ◦ Kelvin

Fahrenheit: used in the US Water freezes at 32F, boils at 212F

Celsius: Used Internationally Water freezes at 0C, boils at 100C

Kelvin: Used in science 0 is an absolute zero (the coldest it can be, -

273.15C, or –459.67F

Temperature

From Celsius to Fahrenheit◦ multiply by 1.8 (or 9/5) and add 32

From Fahrenheit to Celsius◦ subtract 32 then divide by 1.8 (or multiply by

5/9) From Celsius to Kelvin

◦ add 273.15 From Kelvin to Celsius

◦ subtract 273.15

Temperature Conversions

C = F – 32 1.8

F = (1.8C) + 32K = C + 273.15

Convert between Celsius and Fahrenheit -8C 15F 15C 75F 20F

Examples

Convert between Kelvin and Celsius -40C

400K

125C

Examples

Energy is what makes matter move or heat up.

Unit of energy is the joule.

Power is the rate at which energy is used.

Unit of power is the watt.◦ 1 watt = 1 joule/s◦ Our electric bills tend to be kilowatt-hour◦ 1 kilowatt-hour = 3.6 million joules

Units of energy and power

Suppose that your utility company charges 7 cents per kilowatt-hour of electricity. How much does it cost to keep a 100-watt bulb on for a week?

Example

The Cullinan Diamond and the Star of Africa- Page 116, #88◦ The largest single rough diamond ever found, the

Cullinan diamond, weighed 3106 carats; it was used to cut the world’s largest diamond gem, the Star of Africa (530.2 carats), which is part of the British crown jewels collection. How much did the Cullinan diamond weigh in milligrams?

◦ In pounds?◦ How much does the Star of Africa weigh in

milligrams?◦ In pounds avoirdupois?

Example

Box page 103

Gems and Gold Jewelry

You purchase a 14-karat gold chain that weigh 15 grams. How much gold have you purchased (in grams)? Bonus: At the current price of gold, how much is the gold in the chain worth?

Is it possible to have jewelry made of 30-karat gold? Why or why not?

Gems and GoldExamples

Electric Bills- Page 115 #76◦ Your electric bill states that you used 970 kilowatt-

hours of energy in September. Determine your total electrical energy use, in Joules. Determine your average power use, in watts. Assuming the power company generated the energy

by burning oil, calculate the amount of oil needed to provide the energy shown on your bill. Give your answers both liters and gallons. (Hint: burning 1 liter of oil releases 12 million joules of energy.)

Example

Hair Dryer Cost◦ You have an 1800-watt hair dryer, which you use

for an average of 10 minutes per day. Your utility company charges 9 cents per kilowatt-hour of energy. How much does it cost to run the hair dryer each day? Each year?

Example