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Dimensional Analysis

When doing calculations we always write each number with its associated units. As you do the calculation the units should cancel so that the final number you calculate also has the correct units. Let's look at some examples.

Donuts cost $2.79 a dozen. How much do 3 dozen donuts cost?

$\left(3 \mbox{ dozen donuts}\right) \cdot \underbrace{\left(\displaystyle \frac{2.79 \mbox{ dollars}}{1 \mbox{ dozen donuts}}\right)}_{\mbox{Conversion Factor}} = 8.37$ dollars

Convert 0.34 cm to µm (micrometers).

(0.34 cm) • (1 m / 100 cm) • (106µm/ 1 m) = 3.4 x 103 µm

In these two examples the conversion factors are exact numbers. That is, they have infinite precision. Conversions factors, however, are not always exact numbers. Let's look at an example using density as a conversion factor to convert between volume and mass.

What volume will 50.0g of ether occupy if the density of ether is 0.71g/mL?


A pitcher throws a baseball at 90 miles/hour. What is the speed in feet/second?


If the distance between the pitcher's mound and homeplate is 60.5 feet, how long does it take the ball to travel this distance?


Homework from Chemisty, The Central Science, 10th Ed.

1.23, 1.25, 1.27, 1.29, 1.45, 1.49, 1.51, 1.53, 1.55