HK CP Chemistry
DIMENSIONAL ANALYSIS AND CONVERSION OF UNITS
This worksheet is intended to show you a useful technique that can simplify your methods of answering conversion problems.
It is important to use a systematic approach with easier problems so that when more difficult problems are encountered, the method
of approach itself does not add to the problem's difficulty.
EXAMPLE: 1 year = 365 days is an equivalency statement and so are the following statements:
1 hour = 60 minutes
1 minute = 60 seconds
24 hours = 1 day
To solve the following problem you will need to use the statements above.
How many seconds are there in 5 years?
The question is 5 years = ? seconds
5 years
X
X
365 days
1 year
X
24 hr
1 day
0 min
X
1 hr
60 seconds
1 min
=
1.577 x 108 seconds
An easier way to write the above problem is shown below, especially when a long series of conversions is needed
5 years
365 days
24 hr
60 min
1 year
1 day
1 hr
60 seconds
1 min
=
1.577 x 108 seconds
Mathematically you find the product of the top series of numbers and divided it by the product of the bottom series of
numbers. (Be sure to use parenthesis for the bottom #’s because you want to divide the top quantity by the total bottom
quantity)
We will also use this method to convert from one SI unit to another SI unit.
Suppose you wanted to convert the mass of a 250 mg aspirin tablet to its equivalent in grams. Start with what
you know and let the conversion factor units decide how to set up the problem. If a unit to be converted is in
the numerator, that unit must be in the denominator of the conversion factor to cancel.
Notice how the units cancel to give the unit grams.
Next, lets try a more involved conversion. Suppose you wanted to convert 250 mg to kg. You may or may not
know a direct, one-step conversion. In fact, the better method (fool proof) to do the conversion would be to go
to the base unit first, and then to the final unit you want. In other words, convert the milligrams to grams and
then to kilograms:
HK CP Chemistry
= 2.50 x 10-4 kg
Make the following conversions using the method of dimensional analysis and show all your work on separate paper.
1.
Convert 16.7 inches to yards (there are 3 feet in a yard)
2.
Convert 84 miles to kilometers (there are 0.6 miles in a kilometer)
3.
Convert 48,987 minutes to years
4.
Convert 50 m to mm
5.
Convert 25 cm to km
6.
Convert 150 g to g
7.
Convert 250 m to km.
8.
How many cm are in 900 feet?
9.
Convert 5.6 L to mL.
10. Convert 35 nm to m.