Transcript Unit 2B 2008x

Standardized 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
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
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.
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Traditionally measuring weight had 3 distinct
sets of units
◦ Troy- jewelers
◦ Apothecary – pharmacists
◦ Avoirdupois – most other commerce
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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.
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How many ounces is 115 pounds?
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How many tons is 115 pounds?
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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?

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?
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103 = 10 x 10 x 10 = 1,000

10–3 =
1
= .001
10 x 10 x 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
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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
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Multiply- add the exponents
 103 x 105 = 103 + 5 = 108
 (10 10 10)(10 10 10 10 10) = 108
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Divide- subtract the exponents
 106  102 = 106 – 2 = 104
 10 10 10 10 10 10 = 10 10 10 10 = 104
10 10
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Powers of powers- multiply the exponents
 (103)2 = 106
 (10 10 10)(10 10 10) = 106
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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
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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
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Page 102
kilo hecto
deca unit deci
centi
When you move to the right, divide.
When you move to the left, multiply.
milli
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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.
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100 centimeters = 1 meter = .001 kilometers
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5000 milligrams = 500 centigrams = 5 grams
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Convert 2345 centigrams to grams
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Convert 34.58 meters to kilometers
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Convert 54.2 kiloliters to liters
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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
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Convert the following
◦ Use Table 2.6, on page 106
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105 centimeters to yards
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150 pounds to kilograms
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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
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Units
◦ Fahrenheit
◦ Celsius
◦ Kelvin
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Fahrenheit: used in the US
 Water freezes at 32F, boils at 212F
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Celsius:
 Used Internationally
 Water freezes at 0C, boils at 100C
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Kelvin:
 Used in science
 0 is an absolute zero (the coldest it can be, -273.15C,
or –459.67F
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From Celsius to Fahrenheit
◦ multiply by 1.8 (or 9/5) and add 32
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From Fahrenheit to Celsius
◦ subtract 32 then divide by 1.8 (or multiply by 5/9)
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From Celsius to Kelvin
◦ add 273.15
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From Kelvin to Celsius
◦ subtract 273.15
C = F – 32
1.8
F = (1.8C) + 32
K = C + 273.15
Convert between Celsius and Fahrenheit
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-8C
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15F
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15C
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75F
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20F
Convert between Kelvin and Celsius
 -40C
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400K
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125C
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Energy is what makes matter move or heat up.
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Unit of energy is the joule.
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Power is the rate at which energy is used.
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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
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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?
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The Cullinan Diamond and the Star of AfricaPage 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?
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Box page 103
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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 30karat gold? Why or why not?
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Electric Bills- Page 115 #76
◦ Your electric bill states that you used 970 kilowatthours 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.)
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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?