Use Conversion factors to Change the Unit Representing an Amount

What is Dimensional Analysis?

Many people think dimensional analysis is super hard. And yes, it can be pretty hard sometimes. But if you find an easy way to do it, you'll love it in no time!

For those who need a reference, dimensional analysis (a fancy name for unit conversion) converts a measurement from one unit to another. For example, what would 6 cm converted to inches be? 🤔

Basic Conversions

These are some conversions that are the basic ones you'll need to know. Depending on the teachers, you may have to memorize these, but generally speaking, you won't have to memorize them.

Length

1 inch = 2.54 centimeters

1 foot = 30.4878 centimeters

1 centimeters = 0.39 inches

1 yard = 0.91 meters

1 meter = 3.28 feet

1 mile = 1.6 kilometer

1 kilometer = 0.6 miles

Mass

1 ounce = 28.35 grams

1 gram = 0.035 ounces

1 pound = 16 oz = 0.45 kilograms

1 kilogram = 2.2 pounds

Volume

1 teaspoon = 5 milliliters

1 milliliter = 0.034 fluid ounces

1 tablespoon = 15 milliliters

1 liter = 2.11342 pints = 1000 cubic centimeters

1 fluid ounce = 30 milliliters

1 liter = 1.057 quarts = 0.26 gallons

1 gallon = 3.79 liters

1 cup = 0.24 liters

1 pint = 0.47 liters

Looking at Tricks

Take the example mentioned earlier, converting 6 centimeters to inches.

What is the unit you need to convert to? Inches. 

What unit are you starting with? Centimeters. 

First, write the given measurement over 1.

Think back for any conversion you recall, or check the list above, that contains centimeters and inches. In this case, your best bet is probably using one of the following two:

1 inch = 2.54 centimeters

OR

1 centimeters = 0.39 inches

Now put the conversions into fractions. These will help with setting up your equation.

You'll then have to match up pairs where both units are in centimeters so that you can cross those units off. 

If you set it up this way, you can cross off the centimeters. 

The main thing you want to do whenever you do unit conversion problems: get rid of units!

Now, if you plug this right into your calculator, you should get approximately the same answers.

The first one turns out to be 2.36 inches, while the second one is 2.34 inches. The reason why the two answers are a bit off is that we rounded the conversion factor. If you use more decimals for the conversion factor, you should get a very close (if not the same) answer ✅. 

The "official" conversion Google gives us is 2.3622 inches.

Multiple Step Conversions

Let’s try a conversion that needs more than two steps! We’ll convert 2000 inches into kilometers. 

First, let's note that there isn't a unit conversion that goes directly from inches to kilometers. We need to use multiple steps. 

The conversions we would need to use are: 

1 inch = 2.54 centimeters

100 centimeters = 1 meter

1000 meters = 1 kilometer

The last two are not conversions introduced before, but they are part of metric conversions that you should memorize (since usually they are not given on tests). 

Let’s set up the initial measurement:

Then the positioning of the conversion factors! Keep flip-flopping until you get them to line up nicely. 

Now cross off the unit pairs to make sure you lined up the factors correctly. 

If you only have kilometers left, that means you did an excellent job since the problem is asking you to find the measurement in kilometers. 

If you multiply everything out correctly, you should get the answer of 0.05 km, which is barely over a twentieth of a kilometer!

Metric Conversions

In case you are unfamiliar with standard metric conversions, here’s a helpful chart:

Image Courtesy of Pinterest

Takeaways

The best way to get super skilled with unit conversions is getting a lot of practice. If you do enough of the practice, not only will you become skilled in flip-flopping, you'll also know how to multiply and convert in your head. Even when using more complicated units, such as in chemistry or physics, the concept and process is still the same.

Unit conversions become fun when everything cancels out! 😉