For instance, it's common knowledge that there are 12 inches in 1 foot, which is called a unit factor. Unit factors are made up of two measurements that describe the same thing. You can use this fact when translating one rate or measurement.
Here's an example involving unit factors where multiple ratios are needed. Imagine that a car is traveling 20 miles per hour (mph) but you need to know how many inches per minute the car is going. This requires knowledge of three unit factors: 1 foot is 12 inches, 5,280 feet is 1 mile, and 60 minutes is 1 hour. Again, start with what you know and then place your converting ratios strategically based on where the units will cancel. Then multiply what's left in the numerator and denominator like regular fractions. Don't forget to simplify at the end.
You don't always use unit factors to convert between measurements. Sometimes you'll be told the relationship between two quantities of measurement, such as miles per gallon in a car. Another example is in scale or model drawings. These depictions represent something that's either too large or too small to draw at a normal size, such as a house or plant cell. The process for dimensional analysis stays the same, but it's important to read the questions carefully to pick out the units of conversion and to figure out what the question is asking you to measure.
Area is always measured in square units, perimeter is measured in linear units, and volume is measured in cubic units.
Practice question
- Cory is a skateboarder and can travel at a speed of 15 miles per hour. How fast does Cory go in feet per minute? A. 1,320 B. 1,750 C. 1,820 D. 4,752,000
Answer and explanation
- The correct answer is Choice (A).
This a converting units problem, and it's important to remember how many feet are in a mile and how many minutes are in an hour. Setting up your ratios you get:
(recall that it's important to place units in opposite places). Simplifying this conversion, you find that Cory travels at 1,320 ft/min, Choice (A). If you misplaced the converting ratios, then you would end up with Choices (B) and (D).
