Unit Conversions. 1liter. Imagine that we want to convert this quantity in quarts to gallons. There are 4 quarts in one gallon. Show your work below:

Transcription

1 IDS 101 Name Unit Conversions In our everyday lives we frequently have to convert from one unit of measurement to another. When we go to the store and some rope is sold as $.50 per foot and we want 18 inches or when we go to the grocery store and compare the price of a liter bottle of soft drink versus a quart of juice we have make these conversions. (No comments on nutrient values here!) If we go to Canada, gasoline is sold in liters and we pay for the gasoline in Canadian dollars. So, how do we make these conversions? The basic idea in unit conversions is that we can multiply anything times one and we will still have the same original quantity. Also, we can create expressions which, when divided, equal one to help us make the conversions. Let s try a simple example: We go to the store to buy 18 inches of rope, but the rope is sold in feet. To make this conversion we have to know how many inches there are in 1 foot. We then set up the following expression: 1foot 18 inches = 1.5 feet 12 inches We have not changed anything because we multiplied the 18 inches times 1. The inches units cancel and we are left with the units of feet. Let s try another one. This time you set it up. Let s convert the 2 liter pop bottle to quarts. We need the conversion, which is that 1 liter = 1.06 quarts. Set up the conversion and determine the number of quarts in a 2 liter bottle quarts 2 liters = 2.12 quarts Imagine that we want to convert this quantity in quarts to gallons. There are 4 quarts in one gallon. Show your work below: 2.12 quarts = 0.53 gallons 4 quarts

2 We can make the conversion from liters to gallons in one-step, as follows: 1.06quarts 2 liters = 0.53 gallons 4quarts This should work out to the same answer you found by doing the steps separately. Again, let s try another example. We walked a distance and counted our steps. We know that each step was 3 feet apart and we had 100 steps. Let s convert that to kilometers. The equalities you will need are 1 foot = meters and 1000 meters = 1 kilometer. Set-up the conversion in the space below and calculate the answer: 3 feet meters 1kilometer 100 steps = kilometers 1step 1foot 1000 meters Try the conversions below and seek help if you have difficulty. A table of equalities is given near the end of this handout. Show your work. 1) How many miles is a 10 kilometer race? miles 10 kilometers = miles 1kilometer 2) A 10-pound bag of flour weights how many kilograms? 1kilogram 10 pounds = 4.54 kilograms pounds 3) If the atmospheric pressure is 1040 millibars, what is that in bars? 1bar 1040 millibars = 1.04 bars 1000 millibars

3 4) You order 10 yards (really cubic yards) of topsoil for your yard. How many cubic feet will that be? 27 cubic feet 10 cubic yards = 270 cubic feet 1cubic yard 5) Your apartment has a floor area of 800 square feet. What is that in square meters? 1sq m 800 sq ft = sq m sq ft 6) How many centimeters are there in 1 foot? 12 inches 2.54 cm 1 foot = cm 1foot 1inch 7) The following yearly rainfall data were collected, but it is difficult to compare them since they are all in different units. Convert them all to inches of rainfall. Show your work. Aberdeen, WA 2.1 yards 3 ft 12 in 2.1 yd = 75.6 inches 1 yd 1ft Cheyenne, WY mm 1cm 1in mm = 14.6 inches 10 mm 2.54 cm

4 Corpus Christi, TX 143 cm 1in 143 cm = 56.3 in 2.54 cm Ellensburg, WA.60 yards 3 ft 12 in 0.6 yd = 21.6 in 1 yd 1ft Forks, WA 3.3 meters 1ft 12 in 3.3 m = in m 1ft Glendive, MT 298 mm 1cm 1in 298 mm = 11.7 in 10 mm 2.54 cm New York City 1.14 meters 100 cm 1in 1.14 m = 44.9 in 1m 2.54 cm Seattle 96.8 cm 1in 96.8 cm = 38.1in 2.54 cm

5 8) You drive to Canada and the speed limit sign says 90 km/hr. What is that in miles/hr? (hint: do just the conversion on the numerator since the dominator stays the same!) The numerator would be: miles 90 km = 55.9 miles 1km So, the speed limit would be 55.9 miles per hour 9) On your same trip to Canada, you buy some gasoline at $.65 per liter (Canadian dollars). What is that in price per gallon in US funds? 1.39 C$ 1US$ 1.18 C$ 3.79 liters = 4.46 US$ per gallon of gasoline 10) What is the price of gasoline in US$/gallon in Germany if the gasoline sells for 0.92 Euro per liter: 1.41 Euro 1US$ 0.83 Euro 3.79 liters = 6.38 US$ per gallon of gasoline

6 Equalities: Distance: 1 foot= 12 inches 1 inch = 2.54 centimeters 1 foot = meters 1 kilometer= miles 1 kilometer= 3281 feet 1 mile = kilometers 1 yard = 3 feet 1 meter = 1000 millimeters (or 100 centimeters) Area: 1 square meter = square feet 1 square mile = 2.59 square kilometers 1 square mile = 640 acres Volume: 1 cubic centimeter= 0.06 cubic inches 1 cubic inch = cubic centimeters 1 cubic meter = cubic feet 1 gallon = 3.79 liters 1 liter = 1000 cubic centimeters 1 cubic yard = 0.76 cubic meters 1 cubic centimeters = 1 milliliter 1 liter = 1000 milliliters 1 cubic meter = 1,000,000 (1 X 10 6 )cubic centimeters Pressure: 1 bar = 1000 millibars 1 bar = 0.99 atmosphere Mass: 1 pound = 0.45 kilograms 1 kilogram = pounds 1 ounce = grams Monetary: (as of October 24, 2002) 1 US Dollar= 1.27 Canadian Dollars 1 US Dollar= 0.78 Euros