SYSTÈME INTERNATIONAL
also known as SI or the Metric System

When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.   — William Thomson (Lord Kelvin)

As Lord Kelvin stated, it is through the process of measurement that science advances. In order to make measurements, though, we have to have some system of units, standard quantities that everyone knows. For example, if you are measuring your own height, you would likely use feet or centimeters. If you are five feet tall, that means you could stack five standard "feet" to match your own height. Since other people know what "feet" are, they would understand how tall you are. There's nothing to prevent you from inventing your own system of units, but it wouldn't be very useful if other people didn't know it. If you tell someone that you are 17 "fizbits" tall, that statement is meaningless unless they know what a fizbit is!

What sorts of things do we measure in science? The obvious things are length, mass, and time, but there are others, such as temperature, force, speed, acceleration, momentum, energy, and many others. Each of these quantities has units that are used to measure it. For example, here are some units of length: feet, meters, toise, miles, nautical miles, yards, furlongs, hands, fathoms, ells, lightyears, and rods. There are many more. See the Wikipedia category: Units of Length if you're really curious.

In the U.S., most people grow up using the old English system of units: miles, yards, feet and inches for lengths and distances; pounds and ounces for weight (not mass); gallons and ounces for volume. I usually call these "barbaric" units, because they date from medieval England. Parts were inherited from the Germanic tribes that conquered England after the Romans left in 410 AD. (In fact, the name "England" derives from the name of one of those tribes, the Angles.) And some units were Roman in origin, brought to England again by the Norman conquerers after 1066.

In this course we'll sometimes use English units, but usually we'll use the International System of Units, known officially as S.I. from its French name Système International. Many people in the U.S. refer to it as "the metric system".

The Basics   The Metric System is easier than the English units you probably grew up with! If you think the old English system is easy, answer these questions:

• How tall are you — in inches?
• How many yards are there in a mile?
• How many fluid ounces in a gallon?
• Is that a U.S. gallon, or an Imperial gallon?

The reason you may think the English system is easier is that you have an intuitive grasp of the basics — you know about how fast 60 mph is, how much a gallon of milk weighs, how long it takes to walk a mile. You know these things at a gut level. The problem comes when you try doing anything unusual or quantitative. In cooking, for instance, sometimes I've had to figure out how many tablespoons there are to a cup, and how many cups to a gallon. Do you know? If you try doing physics with these units, you end up spending more time converting units (changing a measurement from one unit to another) rather than working on the problem at hand. What's worse, the usual English system doesn't make important distinctions between certain quantities, like mass and weight. So when doing physics with this system, you have to be careful what you mean.

The key to making the metric system easy is to make it intuitive, just like gallons and feet. You've certainly used those 2-liter soda bottles. In fact, that's just about half a gallon. But don't think of it that way, just remember how heavy that 2-LITER bottle was, how many glasses you had to pour to empty it, and how much it hurt that time you dropped it on your foot. A meter is about the same as a yard (actually, it's about 4 inches longer). So a football field is about 100 meters long, and ten football fields is about a KILOMETER, or a little over half a mile.

Activities & Practice
to do as you read

Discussion   On to the details. The base units are the meter (for length), the gram (mass), and the second (time). The meter was mentioned above, about one yard. The gram is about the mass of a paper clip, and a second is 1/60th of a minute, which is itself 1/60th of an hour.

Larger and smaller units are derived from these by multiplying or dividing by powers of ten. Prefixes are then used to modify the unit names. Thus, 1 centimeter = 1/100 of a meter, 1 kilometer = 1000 meters, 1 kilogram = 1000 grams. These prefixes and units are usually abbrevated to specific symbols: 1 kilometer = 1 km, 1 centimeter = 1 cm, 1 kilogram = 1 kg. Here's a table of the most common prefixes.

Other units are derived from the meter, kilogram, and second. For instance, a liter is defined as 1000 cm³ (cubic centimeters), and one unit commonly used for speed is m/sec (meters per second). Units such as these, made by combining the base units (raised to various powers), are called derived units.

The French intended the meter to be one ten-millionth of the distance from the equator to the North Pole. They sent surveying teams out to measure a significant fraction of that distance, and extrapolated (calculated, based on partial information) the full distance. They then had a platinum rod made with two thin engraved lines that distance apart. This prototype was the official, actual definition of the meter until 1960, protected in climate-controlled conditions. The meter is now defined as the distance light travels in 1/299,792,458th of a second. The kilogram is officially defined as the mass of a platinum/iridium prototype held, like the prototype meter, in protected climate-controlled conditions in France. Here's a picture of it, to the right. The prototype was constructed to have a mass equal to the mass of one liter (1000 cm³) of water (at its most dense temperature, 4 °C.)

Memorize this table.

1. A millennium is equal to one thousand years. What is another name for a millenium, using SI prefixes?

Here are a few more comparisons, to help you get a intuitive grasp of these units:

LENGTH
1 millimeter = 1 mm (about the thickness of a dime)
1 centimeter = 1 cm = 10 mm (about the width of a fingernail)
1 meter = 1 m = 100 cm (about a yard)
1 kilometer = 1 km (a little over half a mile)

MASS
1 gram = 1 g (a paperclip)
1 kilogram = 1 kg = 1000 g (a textbook)

VOLUME
1 liter = 1 L = 1000 cm³ (about a quart)

Here are some more comparisons of English and SI units. Memorize the ones in boldface.

Historical Background on SI   SI was born during the French revolution, with first work done in 1790 and its use in France becoming mandatory in 1840. Why would a newborn government, having just overthrown a hereditary king and still entangled in chaos and counterrevolution, concern itself with such a boring topic as weights and measurements. Because France was in financial ruin, and the new government was counting on international trade to provide the commerce and taxes that would support the country. There was a problem, however — every country used a different set of units for measuring goods. Not all countries used "pounds" for weight, for example, and even those countries that called their weight unit the "pound" didn't actually agree on what a pound really was. This made contracts, payments and international trading in general a very slow, difficult and risky business. This situation had been a problem for centuries, of course, but the new government in France decided to finally do something about it.

Interestingly, Thomas Jefferson, the first U.S. Secretary of State under president George Washington, tried to solve this problem at almost the exact same time. In 1790 he proposed a decimal-based measurement system similar to SI. His system did not have a set of mix-n-match prefixes to denote the various powers of ten, so it was encumbered by very many names that were also, confusingly, the same as traditional units. (For example, the foot had ten inches, 1000 feet was a furlong, and 10000 feet made a mile — with none of these equal in length to the traditional inch, foot, furlong or mile.) The proposal was not implemented.

In 1875, the Treaty of the Meter made SI the standard system of measurements for all international commerce. The English system and other systems didn't fade away instantly, of course, but gradually most of the world's countries have adopted SI for all measurements, and today the U.S. and Liberia are the only countries in the world that still commonly use the English system of units in everyday life. Since 1959, the English units “mile”, “pound”, etc. have been defined in terms of the SI standards. Even the English no longer use English units.

Additional Activities & Practice

2. The large SI prefixes tend to be used a lot in talking about computers. For example, a megabyte (MB) is about a million bytes of information. A byte is a unit of information storage, typically the amount of computer memory needed to store one character of text. What is the storage capacity of the hard disk (or disks) on your computer? (To find out, in Windows XP, go to My Computer and hover the mouse pointer over the icons representing each hard disk.)

3. What is the capacity of your computer's RAM? (The RAM is the memory that the computer's processor directly talks to. To find out, in Windows XP, go to My Computer and click on System Information on the upper left of the window. The "General" tab should list the amount of RAM.)

4. Sometimes you will see a computer's memory capacity listed as, for example, 512 mb. What is wrong with that?

5. If you were to express your height in nanometers, would you have a big number or a small number?

6. Find the amount of food in some container at home (box of cereal, canned food, or something similar). On packages in the U.S., usually both English and SI units are given. Record them both.

7. What is a mg? Examine the nutrition information label on the food item. How many mg of salt (it might be called "sodium") does it contain per serving? How many servings are in the container, and what is the total amount of salt in the container?

8. In Homer's Iliad, Paris of Troy absconds with Helen of Sparta, sparking the Trojan War. The Greeks cross the Aegean Sea and lay seige to the city of Troy. Because her kidnapping started this war, Helen's beauty is said to have "launched a thousand ships." Some have proposed therefore that the "helen" be used as a unit of beauty. (a) How many ships could a millihelen launch? (b) How many ships could a decihelen launch?

9. A fortnight is a period of time equal to 14 days. How many seconds are there in a microfortnight?

10. About how long, in seconds, is a nanoyear?

11. What are 2000 mockingbirds equal to?