1. Changing the Units of Measurement
Dimensional Analysis
Changing the Units of Measurement

2. Steps for solving a dimensional analysis problem:
Read the entire problem.
Identify what you have to start with.
Find what units you need to convert into.
Set up your starting value as a fraction with unit(s) on the left.
Set up your ending unit(s) on the far right (after the equal sign).

3. Steps for solving a dimensional analysis problem continued:
Identify a conversion factor that will get you closer to your goal.
Orient the values with units so that cancellation of the units will be possible.
Continue with new conversion factors until only the desired unit(s) remain.

4. Steps for solving a dimensional analysis problem continued:
Multiply all the numerators together and divide by all the denominators.
Double-check that your cancellation has always been done in pairs.
Verify the final unit(s) are what you need.

5. Example #1
16.0 grams of food contain 130 calories. How many grams of food would you need in order to consume 2150 calories?
= ______g

6. Example #1
16.0 grams of food contain 130 calories. How many grams of food would you need in order to consume 2150 calories?
= g

7. Example #2
A person’s weight is 154 pounds. Convert this to kilograms. (1 lbs. = 454 grams) = kg

8. Example #2
A person’s weight is 154 pounds. Convert this to kilograms. (1 lbs. = 454 grams) = 69.9 kg

9. Example #3 An aspirin tablet contains 325 mg of
acetaminophen. How many grains is this
equivalent to? (1 gram = grains)
= __grains

10. Example #3 An aspirin tablet contains 325 mg of
acetaminophen. How many grains is this
equivalent to? (1 gram = grains)
= 5 grains

11. Example #4
Each liter of air has a mass of 1.80 grams. How many liters of air are contained in
2.5 x 103 kg of air?
= ________Liters

12. Example #4
Each liter of air has a mass of 1.80 grams. How many liters of air are contained in
2.5 x 103 kg of air?
= 1,388,889Liters