1. Dimensional Analysis

2. Why use dimensional analysis (DA)?
Dimensional analysis is a technique used to solve problems by converting the units in the question.
For example: How many grams of copper are in 0.5 Liters of copper?
In this question, we need to convert the unit of liters to the unit of grams. How is that done?

3. How do we do DA? Equalities are used to make conversion factors.
Conversion factors are used to convert the given (0.5 L) to the unknown (grams).
The equalities needed for the example given are:
1 Liter = 1000 Milliliters
1 Milliliter = 1 cubic centimeter
1 cubic centimeter of copper = 8.96 grams (density)
These equalities can be used as conversion factors:
1 Liter = 1000 Milliliters → 1Liter or mL
1000 mL Liter

4. Now solve the problem Write down your given. Use conversion factors.
Remember the units must appear on opposite sides of the fraction bar.
Cancel out all units.
Multiply everything in the numerator, and divide everything in the denominator.
0.5 Liters x
1000 milliliter x
1 cm3 x
8.96 grams of copper
= 4480 grams Cu ÷
1 Liter ÷
1 milliliter ÷
1 cm3

5. Try this one on your own.
If Mr. Cope can walk 4 miles every 1 hour, how many feet can he walk in 10 minutes? (1 mile = 5280 ft)
10 minutes
1 hour
4 miles
5280 feet
= 3520 feet
60 minutes
1 hour
1 mile