GSMST – Chemistry Summer Assignment #1
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.
In algebra you learned that if a quantity is multiplied by one, its value does not change. The number one can be thought of as a
quantity divided by its equivalent.
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
This is an equivalence statement (also called a conversion factor) and is equal to 1 so when you multiply it by the original
quantity you are not changing the size or value of the quantity but only changing the unit it is expressed in. Notice that the top
and bottom units cancel each other and you are left with the final unit of 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.
GSMST – Chemistry Summer Assignment #1
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:
= 2.50 x 10-4 kg
Make the following conversions
using the method of dimensional
analysis and show all of your
work on a separate sheet of paper.
1.
Convert 16.7 inches to yards (there are 3 feet in a
yard)
5.
Convert 48,987 minutes to years
2.
Convert 25 yards to inches
6.
Convert 100 miles to inches (there are 5280 ft in one
mile)
3.
Convert 90 centuries to minutes
7.
Convert 1x1020 seconds to year
4.
8.
Convert 84 miles to kilometers (there are 0.6 miles
in a kilometer)
Convert 50 m to mm*
9.
Convert 25 cm to km*
14. Convert 500 nm to km*
15. How many cm are in 5.0 miles ? (1 mile = 5280
10. Convert 400 mm to m*
ft
1ft = 12 in
1in = 2.54 cm )
11. Convert 60 kg to mg*
16. How many nm are in 46 inches?
12. Convert 20 Mg to cg*
17. How many inches are in 300 meters?
13. Convert 150 µg to g*
18. How many cm are in 900 feet?
*For metric conversions use the table on the next page.
GSMST – Chemistry Summer Assignment #1
The way a factor works is in this way. If
you want to know the relationship
between a larger or smaller unit than the
base unit (e.g. meter) you would multiple
1 m by the factor next to the Text and
Symbol for that prefix to equal one of
those units.
Here’s an example:
What is the equality for liters (L) and
microliters (µL)?
1 µL = (1 L)*(10-6 )
or
1 µL = 0.000001 L
or
1 µL = 1*10-6 L
or
6
1*10 µL = 1 L
Any of these methods is acceptable.
Choose the one that makes the most sense to you and stick with it…forever!
Remember to write a unit EVERY time you write a number, and treat them
like you would x or y in algebra class.
In other words units are like variables.
They multiply and divide in the exact same way as algebraic variables.
Example:
Speed * time
(m/s)*s = m [the seconds cancel out because s/s = 1]
If the slash is throwing you off, look at it like this:
m
s =
*
m
s
1