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Converting Units Likely the most useful thing you will learn all year.
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Lecture Part A. ( Just watch and think ) A sign along the road in Canada says “100 kilometers/hour.” What is this in miles per hour?
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1.61 km = 1 mile & 1 km = 0.6214 miles =
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1.61 km = 1 mile & 1 km = 0.621 miles =
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=
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Lecture Part B. ( Just watch and think ) An airplane has a speed of 600 miles per hour. How fast is this in miles per minute?
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=
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=
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=
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= 1 hour = 60 minutes
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=
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= 10 miles/min is the same speed as 600 miles/hour
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= Wait a tick… Why does this method work?
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x ÷ x = ?
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= ?
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= 1
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= This method works because when you multiply by 1 you do not change the value of the quantity. 1
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1a. The piece of paper on your desk is 8 1 / 2 inches by 11 inches. In centimeters, how wide is the page?
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= cm
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How many centimeters equals how many inches? = cm
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2.54 centimeters = 1 inch = cm
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2.54 centimeters = 1 inch
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= 21.6 cm The piece of paper is 21.6 cm wide.
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1b. What is the width of the page, in feet?
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What is the width of the page, in feet? What should we start with: 8.50 inches, or 21.6 cm?
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= ft
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How many feet equals how many inches? = ft
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1 foot = 12 inches = ft
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1 foot = 12 inches
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= ft
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= 0.708 ft The page is 0.708 feet long
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2a. A student is 17 years old. How many hours old is the student?
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=
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= hours
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= 148,920 hours
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2b. How many seconds are in 1 year?
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= seconds
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= 31,500,000 sec
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3a. A sprinter is running at 10 m/s. How fast is this, in miles per hour?
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miles =per hour
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miles =per hour
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miles =per hour
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miles = 22 per hour
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QUICK! How many MPH is the same as 1 meter/second?
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3b. For that same sprinter, how many minutes would it take to run a mile?
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= minutes
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= 1.5 minutes
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4. A hotel room in Paris is 110 Euros. How much is this in US Dollars?
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€110
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= $
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€110 = $
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1 Euro = 1.4 Dollars 1 Dollar = 0.72 Euros €110 = $
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1 Euro = 1.4 Dollars 1 Dollar = 0.72 Euros €110 = $
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1 Euro = 1.4 Dollars 1 Dollar = 0.72 Euros €110 = $ 154
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5. A shoe box is 5 inches x 3 inches x 11 inches = 165 cubic inches. How many cubic centimeters is this?
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= cm 3
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= 2700 cm 3
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6. A car is speeding up at the rate of 1 mph per second. What is this acceleration in m/s 2 ?
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= m/s 2
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= 0.45m/s 2
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7. The density of water is exactly 1 g/cm 3. What is the density of water in pounds per cubic foot?
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= pounds per cubic foot
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= 62 pounds per cubic foot
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8. A truck can unload 100 kg of stone in 2 minutes. How fast is this, in pounds per second?
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= pounds / second
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= 1.8 pounds / second
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9. A landscaper can move 40 kg of soil every 20 minutes. How many hours will it take to move 300 pounds?
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= hours
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= 1.1 hours
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It’s time to extend this method. It can do much more than just conversions.
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10. A baseball pitcher throws the ball at 90 mph. How many seconds does it take for the ball to reach the plate (60 feet away)?
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= seconds
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= 0.45 seconds
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Here’s what you just skipped over: Time = Distance ÷ Speed = 0.45 seconds This means that you can get the right answer to questions, without even knowing the equation. Nice!
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11. The density of a person is 1.4 g/cm 3. The person has a mass of 68,000 g. What is the volume of the person?
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= cm 3
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= 48,600 cm 3 You just used Volume = Mass ÷ Density. You have transcended equations.
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Or, try different ways of combining the quantities, until the units come out right.
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Try different ways of combining the quantities, until the units come out right.
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Estimating ≈
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Which is greater: A.The number of pieces of printer paper, stacked from floor to ceiling. B.The number of walking steps from the High School to the Middle School. C.They are about the same.
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How could we estimate option A.?
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About how far is it from the floor to the ceiling? How tall is a package of paper?
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= sheets
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= 27,000 sheets
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About how far away is the middle school? About how big is one step?
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= steps
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= 3,520 steps
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btw, 27,000 steps ≈ distance from here to Solon, OH
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Which is greater: A.The number of pieces of printer paper, stacked from floor to ceiling. B.The number of walking steps from the High School to the Middle School. C.They are about the same.
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E1a. Estimate how many hours a McDonald’s worker must work to earn enough to buy a car. Assume that all the money goes toward the car. $
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How much is a car? What is the wage of a McDonald’s worker?
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= hours
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= 1000 hours
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E1b. How many years is this?
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= years
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= 0.48 years
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E2. If you drove from here to San Francisco, about how many times would you stop for gas?
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How far away is San Francisco? How far can you drive on one tank of gas? How far can you drive on one gallon of gas? How many gallons fit in a tank?
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= tanks
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= 8 tanks
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E3. If you wanted to buy sliced turkey to feed the entire senior class, how much would that cost?
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How many students is that? How much does each student need? What is the cost, per pound?
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= $
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= $ 500
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E4a. About how many hours have you spent in school?
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How many years have you been in school? How many days in a year? How many hours in a day?
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= hours
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= 15,000 hours
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E4b. About what percentage of your life have you spent in school? %
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How many hours old are you?
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= 150,000 hours
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E4c. What percentage of your waking life have you spent in school?
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How many hours are you awake every day?
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= hours
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= 99,000 hours
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Bonus Question: In your graduating class, how many students (if any!) would you expect to have been born on Friday the 13 th ?
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The chances of being born on a Friday:
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The chances of being born on a Friday: 1 out of 7
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The chances of being born on the 13th:
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The chances of being born on the 13th: 1 out of 30.5
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The chances of being born on the 13th and on a Friday:
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How many seniors were born on the 13th and on a Friday:
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