ccc88 Keeping track of units during conversions can get confusing. Therefore, a

Question

ccc88 Keeping track of units during conversions can get confusing. Therefore, a good strategy is to use dimensional analysis. In dimensional analysis, unit factors are used to cancel out unwanted units and leave the desired units. Consider the following example How many football fields could fit on a 1 mile stretch of land? Here are the relevant conversion factors conversion factor relating miles to meters is 1 mile = 1610 m The speed of light is 3.00 Times 10^8 m/s. How fast is this in miles per hour (miles/h)? The conversion factor relating feet to meters is 1 ft = 0.305 in Keep in mind that when using conversion factors, you want to make sure that like units cancel leaving you with the units you need. You have been told that a certain house is 164 m^2 in area How much is this in square feet?

Explanation / Answer

Part A

1mile = 1610 m

so 1 meter = 1/1610 miles

1 seond = 1/ 3600 hours

Speed of light = 3 X 10^8 m /seconds

3 X 10^8 meters = 3 X 10^8 / 1610 miles

So speed of light = (3 X 10^8 / 1610 miles) / (1/3600 hou r

speed of light = 6.708 X 10^8 miles / hours

Part B

1 feet = 0.305 meters

1 meter = 1/0.305 feet

Or 1m^3 = (1/0.305)^3 feet ^3

the area = 164 m^3

So 164 m^3 = 164 X (1/0.305)^3 feet ^3 = 5776.08 ft^3

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