“From the point of view of teaching and learning, it would not be easy to design a more difficult system than the English system. In contrast, it would seem almost impossible to design a system more easily learned than the metric system.”

-John R. Clark in NCTM’s 1966 yearbook

**The International System of Units (SI) is the simplified modern version of the metric system. It offers enormous advantages for educators:**

**1. No conversions.** The greatest advantage of SI is that it has *only one* unit for each quantity (type of measurement). This means that it is never necessary to convert from one unit to another (within the system) and there are no conversion factors for students to memorize. For example, the one and only SI unit of length is the meter (m). Numerical prefixes may be attached, but they do not form a separate unit. (See *Prefixes* below.)

By contrast, our vast hodgepodge of non-SI (traditional) units makes it very difficult for students to understand quantitative information or the physical world around them. [See Our traditional units nightmare.] Even fundamental concepts like mass, density, and energy are fuzzy for American students because we measure them with so many unrelated units. How does the price of gold (measured in troy ounces) compare with the price of copper (measured in avoirdupois pounds)? How does a water flow measured in acre feet per year compare to a flow in million gallons per day? How does the power of an electric heater (labeled in watts) compare to the power of a gas heater (labeled in Btu/h)? How does the energy of a hamburger (measured in large Calories) compare with the energy of natural gas (measured in therms) or the energy of earthquakes (measured in Richter magnitudes)? For most Americans, such units are essentially meaningless names—names they are unable to employ in practical calculations.

**2. Coherence.** SI units are coherently derived as the simple algebraic quotients or products of a few independent base units, using the same equation as the quantity being measured. There are no numerical definitions or constants for students to memorize. For example, the quantity *power* is defined as *energy per time*. Therefore, the SI *unit* of power (the watt), is defined as the *unit* of power per the *unit* of time:

- watt = joule per second

In symbols,

- W = J/s

**3. No fractions.** SI uses decimals exclusively, eliminating clumsy fractions and mixed numbers.

**4. Prefixes.** Prefixes are short, convenient, unambiguous, easy-to-pronounce names and letter symbols for powers of ten, such as kilo (k) for 1 000, mega (M) for 1 000 000, and giga (G) for 1 000 000 000. Prefixes eliminate long, awkward rows of place holding (non-significant) zeroes. Students can master all twenty prefixes very quickly.

A unit with a prefix attached is called a *multiple* of the unit. *It does not form a separate unit!* A prefix may be changed by moving the decimal point to get rid of unnecessary zeroes. But this should not be called “converting units” since no arithmetic is involved and the unit remains the same. All that is required is an understanding of place value. For example, rewriting 2 000 m as 2 km is analogous to rewriting 2 000 meters as 2 thousand meters. No arithmetic is necessary. A scientific calculator will move the decimal point automatically, if set to ENG display.

**5. Few units.** SI has only about 30 individually-named units, most of which are limited to specialized fields. Students can learn the common units in a very short time.

**6. Easy to write and say.** In general, quantities are much easier to express in SI than in other units. For example, 500 watts (500 W) is much simpler than the many confusing, equivalent, non-SI expressions of power such as 1700 British thermal units per hour (1700 Btu/h), 10 300 large Calories per day (10 300 Cal/d), 120 thermochemical calories per second (120 cal_{th}/s), 22 000 feet poundsforce per minute (22 000 ft·lbf/min), or 0.142 commercial refrigeration tons.

## Should we teach non-SI units?

In March 2000, the National Council of Teachers of Mathematics (NCTM) adopted the official position that SI (metric) should be taught as the “primary measurement system” in schools. Of course, SI is essential in science, and it is increasingly used in other fields as well. Students who are not competent in SI will be at a competitive disadvantage. This is especially true for higher-paying jobs in technology and multinational business. Fortunately, SI can be mastered very quickly if it is properly taught, building up from the base units and prefixes.

But what about the hundreds of non-SI (traditional) units that are still used in the United States? [See Our traditional units nightmare.] Some may survive for years to come, and students will encounter them in the workplace or everyday life. However, to be fluent in them, students would have to memorize hundreds of complex definitions, equations, and multi-digit numbers. Clearly this is an impossible task. The schools can’t hope to teach more than a tiny fraction of the non-SI units a student might need, even for simple calculations like area and volume.

Mathematics courses today usually teach a few, token non-SI relationships, such as 12 inches = 1 foot, 3 feet = 1 yard, and 16 ounces = 1 pound. But this isn’t nearly enough information to do real-world problems. For example, if a rectangular aquarium measures 10 by 10 by 20 inches, how many gallons does it hold? If a lot measures 100 by 200 feet, how many acres is it? Should we spend valuable class time explaining the numbingly complex gallon and acre?

- 1 U.S. gallon = 231 cubic inches = 128 U.S. fluid ounces = 256 tablespoons = 768 teaspoons = 16 cups = 8 U.S. fluid pints = 4 U.S. fluid quarts = 1/31.5 U.S. federal barrel = 1/42 oil barrel = 1/55 drum
- 1 acre = 43 560.17 square feet (approximately) = 1/640 square mile (approximately) = 4840.01 square yards (approximately) = 160 square rods = 10 square chains = 1/10 square furlong = 100 000 square links

Furthermore, by arbitrarily teaching a few non-SI units and ignoring the rest, we give students a false sense of understanding. For example, they don’t realize that a “pound” of force is entirely different from a “pound” of mass or a “pound” of pressure, or that “ounces” of soft drink are volume units unrelated to “ounces” of mass, or that an “ounce” of gold or silver is approximately 1/14.583 pound, not 1/16 pound.

Certainly, we should teach those few non-SI units that are common worldwide and officially approved for use with SI, such as hours and minutes of time and degrees of angle. Students must also understand the *process* of converting from one unit to another, sometimes called the “factor label method.” But teaching measuring units should not be reduced to a tedious exercise in conversion or rote memorization of numbers.

**Contributed by:**

Dennis Brownridge

The Orme School

Mayer AZ 86333

**A PDF containing a PowerPoint-like slide presentation**, for readers who wish to present this material to others, has also been prepared by Dennis Brownridge: Teaching SI: The International System of Units (PDF, 176 kb, 9 slides).

We invite you to become a member of the U.S. Metric Association so you can keep up with metric developments via its bi-monthly newsletter, which is called *Metric Today*. A sample copy of *Metric Today* is also available upon request.

For teaching the metric system, a list of the SI-metric units and symbols, plus more details on their use is given in USMA’s *Guide to the Use of the Metric System*.