1 1 m. 3.2 m 1 cm. 1 m. 1 1 cm. 1 1 = 320 cm. 1 1 m
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1 Activity 1-5 Unit Conversions The factor-label method was developed to keep track of units in multi-step conversion problems. In the method, equalities (i.e., conversion factors) are set up in fraction form. The equalities are then lined up sequentially and units used on the top and bottom of neighboring fractions are alternated so that units cancel. This method is useful not only for doing simple unit conversions (i.e., inches to meters) but it is also useful for guiding us in calculating other quantities such as fuel efficiency of cars or relative costs of food items. Start with the following example: convert 3.2 m into centimeters. The factor-label method works on the simple fact that you can multiply or divide and quantity by 1 and it will not change it. Start by writing the quantity that you are given, in this example 3.2 m, and divide it by m 1 For the next step, multiply this fraction by m 1 1 One can be written as a fraction; 1 = ) = * )+,,,,,,, = = ) - ) * )+,,,,,,, fraction that has the same units as the quantity you are given. 3.2 m 1 m 1 1 m =./0123/4 ) Replace the 1 with a We know that 1 cm = m. This can be written as either ) ),9: - or as ) ;-. Pick the ) ;- ) ), 9: - fraction where you can factor the units. Since meters in the numerator in the first fraction, <.= - pick the fraction that has meters in the denominator,. ) ), 9: m 1 cm 1 1 m Since meters are in both the numerator and the denominator they will factor out. 3.2 m 1 cm 1 1 m When multiplying fractions all of the numbers in the numerator multiply and all of the numbers in the denominator divide. Enter into the calculator = 320. We can of course ignore the ones since multiplying or dividing by one does nothing. The units for this answer are the units that have not factored out, in this case centimeters. 3.2 m 1 cm 1 1 = 320 cm m Sample Problem 1: Convert 87 cm into meters. Strategy: Find conversions that will allow you to get from centimeters to meters. Given: 1 cm = m. This can be written as either ) ),9: - or as ) ;-. ) ;- ) ), 9: - Solution: 87 cm 1 10@= m = 0.87 m 1 1 cm ) ;- ),
2 Sample Problem 2: Convert 9.00 hours into seconds. Strategy: Find conversions that will allow you to get from hours to seconds. Given: 1 hour = 60 minutes 1 minute = 60 seconds Solution: 9.00 hr 60 min 1 1 hr 60 s = s 1 min Sample Problem 3: Convert 55 kilometers per hour (55 km/hr) into meters per second (m/s). Strategy: You need to find conversions that will allow you to get from miles to meters and from hours to seconds. Given: 1 kilometer = 1000 m 1 hour = 60 minutes 1 minute = 60 seconds Solution: 55 km 1 hr 1000 m 1 km 1 hr 60 min 1 min = 15 m/s 60 s The answer is rounded to 15 m/s giving the answer the same number of digits as the original speed of 55 km/hr. 1. A football field is 100 yards long, what is that distance in meters? 2. The Willis Tower in Chicago is 1729 feet tall, what is that in millimeters? 3. A typical human hair is 100 micrometers (µm) wide, what is that width in inches? 4. Pluto averages astronomical units (AU) from the sun, what is that distance in miles? 5. Pluto orbits the sun with a period of years, what is its period in seconds? 6. A school year is defined as minutes of instruction, what is that time in days? 7. The orbital period of the moon is 29.3 days, what is that period in weeks? 8. The distance from Bakersfield to Sacramento is 285 miles, what is that distance in megameters? 9. The speed limit on Interstate 5 is 70 miles per hour (mi/hr), what is that speed in kilometers per hour (km/hr)? 10. A laboratory cart is measured to be moving at 3.4 meters per second (m/s). What is that speed in miles per hour (mi/hr)? 11. You measure the mass of a dime as g. What is its mass in kilograms? 12. A dime has a value of 10. What is its value in dollars? 13. The speed of light is defined as m/s. Convert that into kilometers per hour. 14. A light-year is the distance that light travels in one year. Find that distance in meters. (Hint: convert the speed of light from above into meters per year.)
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