Practical Guide to the International System of Units (SI) Table 1 Prefixes Table 2 SI Units Symbol Prefix Factor Symbol Unit Name Quantity (general symbol ) Definition 24 Y yotta 10 General Purpose 21 Z zetta 10 m meter length ( l) BASE UNIT 18 E exa 10 kg kilogram mass ( m) BASE UNIT 15 P peta 10 s second time ( t) BASE UNIT 12 T tera 10 K kelvin temperature ( T) BASE UNIT G giga 10 9 m² square meter area ( A) m² M mega 10 6 m³ cubic meter volume ( V) m³ k kilo 10 3 N newton force ( F) kg m/s² h hecto 10 2 J joule energy ( E) Nm * da deka 10 1 W watt power ( P) J/s 10 0 = 1 Pa pascal pressure ( p) N/m² d deci 10 –1 Hz hertz frequency 1/s * c centi 10 –2 Electromagnetic C coulomb charge ( Q) As ≈ 6.24 × 10 18 e m milli 10 –3 A ampere current (I) BASE UNIT = C/s µ micro 10 –6 V volt voltage ( V) J/C = W/A n nano 10 –9 Ω ohm resistance ( R) V/A –12 p pico 10 S siemens conductance ( G) 1/Ω = A/V –15 f femto 10 F farad capacitance ( C) C/V –18 a atto 10 Wb weber magnetic flux Vs –21 2 z zepto 10 T tesla magnetic flux density Wb/m –24 y yocto 10 H henry inductance ( L) Wb/A * The four shaded prefixes (hecto, Dimensionless deka, deci, and centi) are irregular amount of substance (n) BASE UNIT mol mole 23 in that they are not powers of 1000. (number of particles) = g/Da = g/u ≈ 6.02 × 10 They are generally limited to cm, rad radian plane angle 1/2 π of a circle m², and m³. See sections 4, 5, 7, 8. sr steradian solid angle 1/4 π of a sphere Powers of two—the binary numbers Visible Light used in computers—have their own corresponding system of prefixes, lm lumen Luminous flux cd sr = 1/683 W @ 540 THz modeled on SI although they’re not SI: cd candela luminous intensity ( ) BASE UNIT = lm/sr 60 I Ei exbi = 2 ≈ 1.15 E 2 Pi pebi = 2 50 ≈ 1.13 P lx lux illuminance ( E) lm/m Ti tebi = 2 40 ≈ 1.09 T Gi gibi = 2 30 ≈ 1.07 G Radiology & Biochemistry 20 Mi mebi = 2 ≈ 1.05 M Bq becquerel radioactivity 1/s (decays per second ) Ki kibi = 2 10 ≈ 1.02 k Gy gray absorbed dose ( D) J/kg ( of body mass ) Sv sievert dose equivalent ( H) Gy Q (Q = quality factor ) © 2006 by Dennis Brownridge Revised 2008-01-28 13:25 kat katal catalytic activity mol/s 2 Understanding measurement and SI Rules. For clarity and simplicity, there are international 1. Advantages and history rules for expressing measurements, summarized in Table 7 The International System of Units, abbreviated SI , is the (pages 12 & 13) with correct examples and common mis- simplified modern version of the various metric systems. takes. Study them carefully. You will encounter errors, Most metric units are not part of SI, so don’t call it “the even in textbooks. Follow this guide, not the textbooks. metric system.” SI has many advantages: • No conversions. Only one unit for each quantity. 2. Base & derived units (Table 2) • No numbers to memorize. Derived units are defined A quantity is a physical measurement, such as length, without numerical factors. time, volume, area, energy, temperature, and mass. Hun- • No fractions. Decimals only. dreds of different quantities are used in science, technol- • No long rows of zeroes . Prefixes replace them. ogy, and everyday life. Quantities are represented with • Complete. SI can measure any physical quantity. italic letter symbols. A specific quantity consists of a num- • Coherent. Units follow natural laws and can be ma- ber times a unit. A unit is a standard of measurement. Units nipulated algebraically. are represented with normal (upright) letter symbols. For • Only 30 units. Compared to hundreds of non-SI units. simplicity, we usually write units with symbols rather than • Clear symbols. Unique, unambiguous letter symbols. spelling them out. For example, 5 m is a quantity (length) • World standard. Virtually all measurements are based consisting of the number 5 times the unit meter (m). Write on SI, even if expressed in other units. symbols exactly as they appear in the tables. They are sym- bols, not abbreviations, and are case sensitive. Always Non-SI units. Any unit not on Table 2 (page 1) is a non-SI leave a space between the number and unit. (See Rules 2 unit. Hundreds of them are in use, especially in the USA. through 11, pages 12 & 13.) They include a chaotic hodgepodge of old metric, Babylo- nian, and European units, plus units invented for various SI is built on seven fundamental standards called base industries and scientific fields. None of them are really nec- units , included in Table 2 (page 1) and defined in Table 9 essary, since all physical quantities can be measured in SI. (page 14). All other SI units are derived by multiplying, dividing, or powering these base units in various combina- History. SI was introduced in 1960. However, its roots go tions. No numerical factors are involved (except for the back a century earlier when British scientists developed the sievert). SI is a coherent system, which means that derived first coherent measurement system, based on physical laws units are defined by the same laws or equations as the and metric base units. SI is governed by the General Con- quantities they measure. For example, the quantity called ference of Weights and Measures (CGPM), an international speed ( v) is defined as distance per time . Per means treaty organization founded in 1875. The United States is a “divided by.” Distance is a kind of length. In symbols, charter member. The names of most SI units (those with capitalized symbols) honor the scientists who discovered v = d/t (definition of speed) the laws for the corresponding quantity. It is truly an inter- national system. Only two of the 30 SI units (meter and The SI unit of speed is therefore meter per second —the kilogram) were part of the original metric system intro- unit of length divided by the unit of time. In symbols, you duced in France in the 1790s. can show division three different ways: a slash, horizontal bar, or negative exponent. For example, you may write “8 SI in the United States. Americans were intimately in- meters per second” as 8 m volved in developing SI. For example, the energy and elec- 8 m/s 8 m s–1 s trical units (joule, watt, volt, ampere, etc.) were established at conferences in Chicago in the 1880s. But paradoxically, The slash and negative-exponent styles keep everything the United States is virtually the only nation where anti- neatly on one line, while the horizontal-bar style is useful quated non-SI units still predominate in everyday life. The in calculations, for ease in canceling. U.S. Constitution (Article I, section 8) gives Congress the job of establishing a measuring system. After detailed stud- To multiply unit symbols, use a middle dot ( ), Unicode ies, Congress legalized metric units in 1866. Since 1893, all character 00B7. Don’t pronounce or spell it out. Example: American measuring units have been based on SI stan- dards. In 1975 and 1988, after still more studies, Congress 15 N m ( pronounced “15 newton meters”) adopted SI as the preferred U.S. system, but failed to pass effective laws enforcing it. Nevertheless, a growing frac- See Rules 13 and 14, page 13. tion of the American economy is now largely SI, including automobiles, heavy equipment, farm machinery, medicine, science, electronics, computers, cameras, bicycles, the mili- tary, and several sports. 3 and down) have lowercase symbols and mostly end in “o.” 3. Characters not on the keyboard The symbol is the first letter of the name, except for µ SI requires four characters not shown on a computer key- (micro) and da (deka). The letter µ is the Greek “m,” called board. In any application, you can insert them by holding mu, which is Unicode character 00B5. Be sure to write let- down the Alt key while you type a four-digit code on the ters carefully. There is a big difference between M (mega = number pad (fourth column of Table 3 below). Num Lock 10 6) and m (milli = 10 –3), and an even bigger difference be- must be on. However, in Microsoft Word™ it’s much eas- tween P and p, Z and z, and Y and y. ier to use shortcut keys, which are easily to set up. Click Insert, Symbol, enter the Unicode character number, click Regular prefixes. Choose a prefix that minimizes place- Shortcut Key, press the desired shortcut keys, Assign, holding, non-significant zeroes (Rule 12, page 13). Most of Close. Thereafter, you can insert the symbol by just press- the prefixes are multiples of a thousand, or 10 3 (10 3, 10 6, ing the shortcut key. The key assignments in the right hand 10 9, 10 12 , etc.) These regular prefixes, shown without shad- column of Table 3 are recommended, so you won’t disable ing on Table 1, may be used with any SI unit. Think of any of Word’s default shortcuts. For combinations you use them as a ladder. Going up the ladder multiplies a unit in frequently, the AutoCorrect feature is even easier (Tools, steps of 1000 or 10 3. Include 10 0 (=1) as a step, although it AutoCorrect Options...).