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Metric Conversion Using Dimensional Analysis Worksheet

This worksheet is designed to give you practice using dimensional analysis for converting from one unit of measurement to another. Show all of your work.

Analyze – write this information from the problem

Known ------( equivalents ------- > unknown

Part 1 Dimensional Analysis – goal post method

1. Draw a horizontal line and two vertical goal posts creating two compartments.

2. Write the known with unit as a fraction over 1 in the first compartment.

3. Drag and drop the unit of the known to the denominator of the next compartment

4. Write an equivalent that has the known unit in the denominator in this compartment.

5. Cancel the identical units that appear in the numerator of the known and the denominator of the equivalent.

6. Continue to drag and drop the unit of the equivalent to the denominator of the next compartment until you get to the desired unit. This may take many steps.

7. Once you reach the desired unit you should only have one unit not canceled, the desired unit.

Perform the following conversions using dimensional analysis. SHOW YOUR WORK IN THE SPACE PROVIDED UNDER EACH LETTER. !!

A) 75 Km = ? m

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B) 26,800,000 µm = ? m

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C) 11,200,000,000 µL = ? L

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D) 37.687 yds = ? in

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E) .00898 km = ? cm

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F) 89,800,000,000,000 µm = ? km

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Write your own set of instructions of how to use the method of dimensional analysis to convert from one unit to another.

Metric to Metric Conversions

(Note: Conversion factors have unlimited significant figures so NEVER use conversion factors to determine significant figures in your answer. Always use the original numbers given in the problem to determine significant figures of the final answer)

1. How many centimeters are in 4.12 meters?

2. How many kilometers are in 8432 meters?

3. Change 3.24 kilometers into meters.

4. How many millimeters are in 25 meters?

5. How many millimeters are in 251 centimeters? (2 step problem)

English to English and Metric to English Conversions

1. How many inches are in 7.86 ft?

2. How many feet are in 256 inches?

3. How many quarts are in 25.78 gallons?

4. How many centimeters are in 12.0 inches?

5. Change 25,678 pounds into tons.

6. How many millimeters are in 1.12 feet? (multi-step problem)

ENRICHMENT (only do this if you are confident with pages 1-4)

1. How many inches are in 5.6 miles?

2. How many millimeters are in 1.23 gallons?

3. A chocolate bar weighs 4.00 ounces. If the chocolate delivers 2.78 calories per gram, how many calories are in the chocolate bar?

4. In order to gain one pound of body weight, the average person must consume 3500 more calories than he/she uses. Assuming you are totally sedentary and burning no calories, how many chocolate bars would you need to eat to gain 5 pounds (use the answer from #3 to calculate).

ENRICHMENT - Using Dimensional Analysis to Solve Problems Using Cubic Volumes

How to figure out conversion factors with cubic units:

1 cubic cm = 1 cm3 = 1 cm x 1 cm x 1 cm

1 cubic inch = 1 in3 = 1 in x 1 in x 1 in

Example:

How many cubic centimeters are in 1 cubic inch?

1 inch x 1 inch x 1 inch x 2.54cm x 2.54cm x 2.54cm = 16.4 cm3

1 1 in x 1 in x 1 in 1

Try these:

1. How many cubic inches are in 3.00 cubic feet?

2. How many ft3 are in 1 yd3?

3) You visit the store and find a banana sale. On average 8 bananas weigh one pound. The sale price for bananas is four pounds for $5.00. You decide to treat your advising group to 25 banana splits, 1 banana per split.

A) Write the equivalence statements.

________________bananas = 1 lb _______________lbs = _________________ dollars

B) How much will it cost you to buy 25 bananas?

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4) The average length of a hotdog is 12.0 cm. The distance to the moon is 3.84 x108 meters. How many hotdogs must you line up to reach the moon?

A) Write the equivalence statements

________ hot dog = _______ cm __________ m = __________cm

distance to moon = __________________ m

B) How many hotdogs must you line up to reach the moon?

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5) The distance to the sun is 1.496 x1011 meters. The speed of light is 3.00 x108 m/s. A minute is defined to be 60 seconds.

A) Write the equivalence statements:

Distance to sun = ________________ m Speed of light = ____________________m/s

______________minute = _____________seconds

B) How long does it take for light to get from the sun to the earth?

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6) If the density of mercury is 13.6 g/ml, find the A) mass of 43.0 ml of mercury, B) volume of 43.0 grams of mercury. (Hint: use the density of mercury to write an equivalence statement between mass and volume.)

________________= ________________

A) Mass of 43.0 mL of mercury

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B) Volume of 43.0 grams of mercury

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7) You exhale about .0800 liters of CO2 (carbon dioxide) gas in a single breath. 22.4 liters of CO2 contain 6.022 x 1023 molecules. 6,022 x 1023 CO2 molecules have a mass of 44.0 grams.

Find the:

A) number of carbon dioxide molecules you exhale in each breath.

B) Find the mass of the CO2 you exhale in a single breath.

________________= ________________ ________________= ________________

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8) The density or of carbon dioxide is 1.98kg/m3. Express the density of carbon dioxide in grams/ cm3

9) The density or of gold is 19.3 g/cm3. Express the density of gold in in kg/ m3

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