In medieval times, an team of ox could plow a furrow in a day. How long is this furrow as measured in meters?
To do this you would use a technique called dimensional analysis. (Sometime this system is also called the "factor label" system.) This technique uses the units or dimensions of the numbers to create a math relationship that will allow you to switch between units. This is done by changing equations to fractions.
If you had the following setup, how would your math teacher show you to solve it?
An equality describes two concepts as being equal. The statement, "5280 feet = 1609 meters," is an equality. The "Fact Sheet" lists many equalities that will be used in class. This particular fact sheet does not show all the equalities. It shows a collection of equalities that will use most often in this course. (Note there are a few equalities you need to memorize for this course. These equalities will not be appear on any fact sheet passed out for your tests or quizzes.) Equalities can be written as fractions. For example.
This is a useful tool. This means that any unit equality can be written as a fraction. Back to the original question, "In medieval times a team of ox could plow a furrow in a day. How long is this furrow as measured in meters?"
10,560 ft = 2 miles
Using this equality, write 2 fractions. One with miles in the numerator and the other with feet in the numerator.
The abraviation for feet is "ft," for miles it is "mi." Do not simplify your fractions.
10,560 ft = 2 miles
Using this equality, write 2 fractions. One with miles in the numerator and the other with feet in the numerator.
The abraviation for feet is "ft," for miles it is "mi." Do not simplify your fractions.
24 hr = 3600 s
Using this equality, write 2 fractions. One with hours in the numerator and the other with seconds in the numerator. Do not simplify your fractions.
24 hr = 3600 s
Using this equality, write 2 fractions. One with hours in the numerator and the other with seconds in the numerator. Do not simplify your fractions.
A car is traveling at . That's the same as .
Using this equality, write 2 fractions. One with ft/s in the numerator and the other with mi/h in the numerator.
Your answer will be a huge fraction. Do not simplify.
A car is traveling at . That's the same as .
Using this equality, write 2 fractions. One with ft/s in the numerator and the other with mi/h in the numerator.
Your answer will be a huge fraction. Do not simplify.
It takes a dog 2 hours to wander 17 football fields away from home. What is the dog's displacement in meters? (Work out this problem and check your answer)
The answer is 1554.48 m
All fractions are created using the equalities from the fact sheet. In order to solve this you will have to switch units systems. The conversion to remember when switching between the British customary system and the S.I. system is
2.54 cm = 1 inch
Start the set up with the distance you are given, 17 football fields, and convert to inches then cross over to the metric system.
To solve this on a graphing calculator you would put all the number in numerator in parenthesis and divide it by all the numbers in the demonstrator in parenthesis. Your graphing calculator screen would look something like this:
This is what your answer should look like. Notice how number has a unit next to it and the answer is in a box.
This is a very basic dimensional analysis. In class we will discuss conversion of fractional units and units raised to a power.
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
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. That's the same as 
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