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  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.

 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 Tables 2.1, 2.2 and 2.3  Notice that liquid and dry measure units have the same names but are different sizes.

 How many ounces is 115 pounds?  How many tons is 115 pounds?

 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?

 10 3 = 10 x 10 x 10 = 1,000  10 – 3 = 1 = x 10 x 10

 Positive exponent- the number of zeros after the 1  10 0 = 1  10 2 = 100  = 1 followed by 15 0’s  Negative exponent- the number of values to the right of the decimal  =.1  =.01  = the decimal followed by 14 zeros and then a 1

 Multiply- add the exponents  10 3 x 10 5 = = 10 8  ( )( ) = 10 8  Divide- subtract the exponents  10 6  10 2 = 10 6 – 2 = 10 4  = =

 Powers of powers- multiply the exponents  (10 3 ) 2 = 10 6  ( )( ) = 10 6

 No shortcut, write them out and then add/subtract the values ◦ = ,000 = 10,100 ◦ 10 5 – 10 3 = 100,000 – 1,000 = 99,000

 Designed for 2 reasons ◦ To replace many customary units with just a few basic units ◦ To simplify conversions by using the decimal system

 Page 102 kilo hecto deca unit deci centi milli When you move to the right, divide. When you move to the left, multiply.

 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

 Convert 2345 centigrams to grams  Convert meters to kilometers  Convert 54.2 kiloliters to liters

 State how much larger or smaller the first unit is from the second. ◦ millimeter, deciliter ◦ kilometer, micrometer ◦ cubic meter, cubic centimeter

 Convert the following ◦ Use Table 2.6, on page 106  105 centimeters to yards  150 pounds to kilograms

 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

 Units ◦ Fahrenheit ◦ Celsius ◦ Kelvin  Fahrenheit: used in the US  Water freezes at 32  F, boils at 212  F  Celsius:  Used Internationally  Water freezes at 0  C, boils at 100  C  Kelvin:  Used in science  0 is an absolute zero (the coldest it can be,  C, or –  F

 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  From Kelvin to Celsius ◦ subtract C = F – F = (1.8C) + 32 K = C

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

Convert between Kelvin and Celsius  -40  C  400  K  125  C

 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

 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?

 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?

 Box page 103

 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?

 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.)

 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?