IDS 101Name______

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 types of 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:

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.

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

We can make the conversion from liters to gallons in one-step, as follows:

= ?

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 = 0.3048 meters and 1000 meters = 1 kilometer. Set-up the conversion in the space below and calculate the answer:

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?

2) A 10-pound bag of flour has a mass of how many kilograms?

3) If the atmospheric pressure is 1040 millibars, what is that in bars?

4) You order 10 “yards” (really cubic yards) of topsoil for your yard. How many cubic feet will that be?

5) Your apartment has a floor area of 800 square feet. What is that in square meters?

6) How many centimeters are there in 1 foot?

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, WA2.1 yards

Cheyenne, WY370.8 mm

Corpus Christi, TX143 cm

Ellensburg, WA.60 yards

Forks, WA3.3 meters

Glendive, MT298 mm

New York City1.14 meters

Seattle96.8 cm

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!)

9) On your same trip to Canada, you buy some gasoline at $1.09 per liter (Canadian dollars). What is that in price per gallon in US funds?

10) What is the price of gasoline in US$/gallon in Norway if the gasoline sells for 8.35NK (Norwegian Kroner) per liter?

11) What is the price of gasoline in US$/gallon in Russia if the gasoline sells for 12.88 Rubles per liter?

Exponential Notation:

Sometimes we use very large or very small numbers in science. Sometimes we multiply or divide these large numbers and if our calculators have only have 8 digits we get an error message. We can use exponential notation to make the numbers more manageable.

Exponent / Number
105 / 100,000
104 / 10,000
103 / 1,000
102 / 100
101 / 10
100 / 1
10-1 / 0.1
10-2 / 0.01
10-3 / 0.001

We can represent the number 500,000 as 5 X 105. What would be the exponential notation for 5,400,000? How about 0.123?

To multiply 5.6 X 105 times 4.2 X 107, we multiply the 5.6 times 4.2 = 23.52 and then add the exponents (5 + 7= 12). The answer would be 23.52 X 1012 or 2.35 X 1013 .

For some practice with this concept, let’s use exponential notation to solve the following question:

Imagine that we wanted to know the number of atoms of carbon released into the atmosphere when enough coal is burned to supply Seattle with electricity for a year. (Our assumptions: coal is 75% carbon; there are 6 X 1023 atoms of carbon in 12 g of carbon, 1 ton = 2000 pounds, and we need 6 million tons of coal).

Step 1: convert the tons of coal to pounds

Step 2: Convert the pounds of coal to grams

Step 3: Multiply the product of step two times .75 to get the number of grams of carbon burned.

When combustion occurs, the total input of coal must equal the total output of carbon to the atmosphere. (One of the fundamental “laws” of science is the “conservation” law. In non-nuclear reactions, like burning coal or oil, we do not create or destroy matter. The amount of atoms of carbon in the coal must equal the number of atoms in the emissions from the plant!)

Step 4: Determine the number of atoms of carbon released to the atmosphere

coal is burned.

If you need additional practice manipulating these large numbers, go the following web pages for help with exponential notation:

(click on Problem Generator on the right side of the page for practice problems)

Equalities:

Distance:

1 foot= 12 inches

1 inch = 2.54 centimeters

1 foot = 0.3048 meters

1 kilometer= 0.6214 miles

1 kilometer= 3281 feet

1 mile = 1.6093 kilometers

1 yard = 3 feet

1 meter = 1000 millimeters (or 100 centimeters)

Area:

1 square meter = 10.76 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 = 16.39 cubic centimeters

1 cubic meter = 35.31 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 106 )cubic centimeters

Pressure:

1 bar = 1000 millibars

1 bar = 0.99 atmosphere

Mass:

1 pound = 0.45 kilograms

1 kilogram = 2.205 pounds

1 ounce = 28.35 grams

Monetary: (as of June, 2008)

1 US Dollar= 1.05 Canadian Dollars

1 US Dollar= 5.03NK (Norwegian Kroner)

1 US Dollar= 25.77 Rubles (Russian currency)

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