Units are very important, not only in science but in "real life" as well. Units give numbers meaning. If you are running low on gas between El Paso and Midland, the ambiguous sign "Next Gas 100" can be very important. Is that 100 yards or 100 miles? Getting over a cold would be frustrated by a bottle with the helpful guidelines "Take two twice per day." Two what? Tablespoon? Teaspoons? Bottles?

Units are vitally important to make sense of results in science. In this class, NO credit will be given for answers without units, and reduced credit will be given for answers with incorrect units. Therefore, it will be in your best interest to be aware of and utilize units to their fullest.

Units can also be helpful in determining how to get an answer. For example, we know that velocity (or speed) is typically measured in miles per hour, so we can guess that the formula for calculating velocity is distance (miles) divided by (per) time (hour). This is indeed the case.

The three basic properties of objects are distance (height, width, depth), time (duration), and mass (which is a measure of how much material is in an object). In the "English system" (which is used only in US, ironically) these quantities are measured in the following units:

• distance: inches, feet, yards, miles
• time: seconds, minutes, hours, days, years
• mass: ounces, pounds, tons

All other units, say of area or the abovementioned velocity, are derived from these. How do we go back and forth between these units? We know there are 12 inches in a foot. This is called a conversion factor:

Thus if we wanted to compute the number of inches in 3 feet:

Notice how the foot units cancel to leave us with what we need, inches. You should ALWAYS do unit conversions in this manner; it's a pain to write all those units out just to cross them off, but it will save you time and frustration in finding mistakes.

Here are some more conversion factors:

• 3 feet = 1 yard
• 24 hours = 1 day
• 60 seconds = 1 minute
• 2000 pounds = 1 ton
• 1 year = 365.25 days

Notice how bizarre some of these conversion factors are? Can you recall without looking it up the number of yards in a mile? The number of ounces in a pound? Also many units of antiquity were based on the physical characteristics of the ruling monarch (hence the term foot).

The need for a universally standard and easy to remember system of units led to the creation of the "Systeme Internationale," or metric system:

• distance: meters, centimeters, kilometers
• time: as English system
• mass: gram, milligram, kilogram

All units are standardized across the world. The meter is based on the wavelength of a certain color of light. The second is based on the vibration of a certain kind of atom. The gram is the mass of one cubic centimeter (cc) of pure water (why water?). In addition, the conversion between units is a simple matter of looking at the prefix:

Thus, a kilometer (km) is 1000 meters (m), a milligram (mg) is one one-thousandth of a gram, and a microsecond (ms) is one one-millionth of a second (s). Old habits can be hard to break: a twice-a-week class at ACC lasts an hour and fifteen minutes, not 4.5 kiloseconds!

Conversion between English and metric units is possible but approximate:

• 1 inch is about 2.5 centimeters
• 1 kilogram is about 2.2 pounds
• 1 mile is about 1.6 kilometers

To further complicate matters (and deal with the extreme distances and masses in astronomy), astronomers have invented some units of their own:

• 1 Astronomical Unit = 1 AU = 149,600,000 km = 93,000,000 miles
• 1 light year = 1 ly = 9.46 x 10¹² km = 6 trillion miles
• 1 parsec = 3.26 ly = 206265 AU = 3.09 x 10¹³ km
• 1 Ångstrom = 10^-10 meters
• 1 solar mass = 1.99 x 10³³ gm

Units can save you effort and stress, or they can be a real nuisance. Learn to use them, and make them work for you.

Updated 8/26/99

Copyright Ó 1999 Austin Community College