ORGANIZED APPROACH TO PROBLEM SOLVING USING UNITS Factor Label/ Conversions/ Dimensional Analysis.
Standardized Units: More Problem Solving Power
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Transcript of Standardized Units: More Problem Solving Power
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2BStandardized Units:
More Problem Solving Power
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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
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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
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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
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How many ounces is 115 pounds?
How many tons is 115 pounds?
Converting in USCS units
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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
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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
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103 = 10 x 10 x 10 = 1,000
10–3 = 1 = .00110 x 10 x 10
Powers of 10
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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
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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
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Powers of powers- multiply the exponents (103)2 = 106
(10 10 10)(10 10 10) = 106
Powers of 10 More Exponents
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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
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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
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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
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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
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Convert 2345 centigrams to grams
Convert 34.58 meters to kilometers
Convert 54.2 kiloliters to liters
Examples
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State how much larger or smaller the first unit is from the second.
◦ millimeter, deciliter
◦ kilometer, micrometer
◦ cubic meter, cubic centimeter
Examples
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Convert the following◦ Use Table 2.6, on page 106
105 centimeters to yards
150 pounds to kilograms
Metric-USCS Conversions
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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
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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
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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
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Convert between Celsius and Fahrenheit -8C 15F 15C 75F 20F
Examples
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Convert between Kelvin and Celsius -40C
400K
125C
Examples
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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
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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
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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
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Box page 103
Gems and Gold Jewelry
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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
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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
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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