# 42, Trabucs and the Metric System The Importance of Units

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"In Doug Adams' irresistible novel 'Hitchhiker's Guide to the Galaxy', the answer is 42. But 42 what? Technical, scientific and financial information is mostly expressed in numbers. Forty-two may be the answer to the questions of Life, the Universe and Everything, but without units or other metadata (data about data), it cannot be of much help."

Philippe Theys
Data Quality Manager

Units give sense to numerical data. In the same way as the countries that are members of the European community switched to a single currency, the Euro, at the end of 2001, many attempts have been made over the years to move the world to a single system of units of measurement.

United States Secretary of State Thomas Jefferson asked Congress in 1790 to adopt a decimal system of weights and measures "...and thus bring the calculations of the principal affairs of life within the arithmetic of every man who can multiply and divide plain numbers." A few years later, the French Assembly adopted the metric system to encourage trade within France. Before then, each province had a separate system of units, sometimes using the same name for units representing different quantities. These numerous systems were often of tremendous complexity and ambiguity as shown below:

 13 toises (Paris) = 8 trabucs (Nice) 29 meters = 9 trabucs (Nice) 17 feet (Paris) = 22 pans (Marseille) 5 meters = 19 pans (Nice) 4 toises = 33 cannes (Marseille) 14 pans (Nice) = 33 decimeters 1 arpent (ordonnance) = 22 feet 1 arpent (Paris) = 18 feet 1 arpent (common) = 20 feet

The metric system was introduced in the last years of the eighteenth century, but it was a struggle to have it completely implemented. Several decades passed before it was fully deployed in France, but it is now used in the whole world except for a handful of countries: Bangladesh, Liberia and The United States. The metric system has been improved to incorporate all aspects of physics and has been renamed Système International.

Système International, through many contributions, has evolved into a totally unambiguous and coherent system. When correctly implemented, it labels physical quantities in clear and well-defined terms. Units are each abbreviated in a unique and unambiguous way: an upper or lowercase letter represents one, and only one, quantity or multiple. For example:

 *There are more multiples, or prefixes. Here's the full list, along with their abbreviations: 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deca da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yocto y

The multiples are*:

 m milli 1/1000 or 10-3 c centi 1/100 or 10-2 d deci 1/10 or 10-1 da deca 10 or 101 h hecto 100 or 102 k kilo 1,000 or 103 M mega 1,000,000 or 106 G giga 1,000,000,000 or 109 T tera 1,000,000,000,000 or 1012

The units may be used alone or in combination with the multiples:

 53 g is 53 grams 53 mg is 53 milligrams 53 kg is 53 kilograms 16 m is 16 meters 16 mm is 16 millimeters

Unfortunately, SI is sometimes used with excessive flexibility and lack of discipline. The SI meaning of M is an abbreviation of mega, the Greek word for "large," representing 1,000,000 or 106, while in the United States, M is often understood as the Roman numeral for 1,000. Another common mistake is to ignore the rule concerning multiples and exponents. The exponent applies to the unit and to the multiple. So km2 means km • km or 106m2, which is 1,000,000 square meters. It is not k • m • m, which would be103m2, or 1,000 square meters.
These details may sound a bit mundane and the enforcers of SI may seem narrow-minded, but if an organization or individual gets it wrong, it can be very expensive or dangerous.

Here are a few examples of mistakes induced by a poor control of units:

• A national power company suffered from a mix up between prices quoted in kilo-Watt-hour (kWh) and therms. It committed itself to paying US\$800,000 for gas worth US\$50,000, while trading on the market.
• In Canada, a plane ran out of fuel because the pilot mistook liters for gallons! The passengers were lucky that the captain was better as a glider pilot than he was with units. He landed the plane safely without power on an emergency airstrip.
• More recently, the Mars Climate Orbiter, a NASA spacecraft, swooped in too low as it headed for Mars orbit, dipped too deeply into the atmosphere and was never heard from again. When a NASA contractor told the navigators how much force the thrusters had applied to the spacecraft, they used units of pounds; while NASA assumed the data were in newtons.

So you may find that the answer is 42, but make sure you know what the units are.