Dimensional Analysis Practice

Dimensional analysis is a systematic method of problems solving. The approach is based on including

complete units with all numbers in a problem and performing the same arithmetic steps with the units that

you perform with numbers associated with them. Below are some examples that illustrate how to use

dimensional analysis. Follow these examples to learn the common pattern apparent in applying this

approach

Steps to solving Dimensional Analysis problems:

1.

What are your starting and ending units?

2. Develop a unit plan.

3. Select appropriate conversion factors.

4. Cancel units and check.

5. Do math on calculator by multiplying all numbers on the top, then multiplying all numbers on the

bottom, and finally dividing the top number by the bottom number.

See the examples below for how to use these steps.

1. What units would the answer be in?

1 mile X 5280 ft x 12 inches = XX

1 mile 1 foot

2. An automobile travels at an average speed of 50 km per hour. How long will it take

for the car to travel 850 km?

Solution:

Determine what units are given

Determine what unit your answer should be in

Determine your conversion factors

.

850 km given

Answer to be in hours how long will it take?”

• Average speed of 50 km per hour can be rewritten as 50 km = 1 hour

• Possible conversion factors (written as a fraction)

50 km

or 1 hour

1 hour

50 km

Given quantity X conversion factor(s) = sought quantity

XX

XX

hours

3. How many seconds are there in 3 years? (Assume a non-leap year!)

Solution:

Determine what units are given:

xx

Determine what unit your answer should be in: XX

Determine your conversion factor(s). Use simple easy ones!

XX

Now set up your probleml! Remember this includes numbers as well as units

XX XX

XX

XX

XX

х

х

х

х

XX

XX

XX

XX

XX

XX

XX