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The System of Measurement

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The System of Measurement THE SYSTEM OF MEASUREMENT CONTENTS 1 General 2 International System of Units (SI) 3 Length 4 Area 5 Volume 6 Capacity 7 Weight 8 Time 9 Temperature 10 Angular and Circular 11 Miscellaneous 12 Cross Conversion Table 13 Calculation Formulae 14 Abbreviation 1. G E N E R A L ========================================================================= 1.1 NUMBER SYSTEM ------------------------------------- System Base of Radix ------------------------------------- Binary Two Ternary Three Quaternary Four Quinary Five Senary Six Septenary Seven Octonary (or Octal) Eight Novenary Nine Decimal Ten Undecimal Eleven Duodecimal Twelve Terdenary Thirteen Quaterdenary Fourteen Quindenary Fifteen Sextodecimal Sixteen Septendecimal Seventeen Octodenary Eighteen Novendenary Nineteen Vicenary Twenty Tricenary Thirty Quadragenary Forty Quinquagenary Fifty Sexagenary Sixty Septuagenary Seventy Octogenary Eighty Nonagenary Ninety Centenary Hundred ------------------------------------- 1.2 STANDARD SYSTEM OF SCIENTIFIC NOTATION (DECIMAL SYSTEM OR PREFIXES SYSTEM) ------------------------------------------------------------------------- ----- Prefix Symbol Value Submultiples and Multiples ------------------------------------------------------------------------- ----- atto (at' to) a .000 000 000 000 000 001 1x10- 18 femto (fem' to) f .000 000 000 000 001 1x10- 15 pico (pe' ko) p .000 000 000 001 one-millionth millionth 1x10- 12 nano (nan' o) n .000 000 001 1000 of a millionth 1x10-9 micro (mi' kro) u* .000 001 one-millionth 1x10-6 milli (mil' i) m* .001 one-thousandth 1x10-3 centi (sen' ti) c* .01 one-hundredth 1x10-2 deci (des' i) d .1 one-tenth 1x10-1 deca (dek' a) da 10 ten 1x101 hecto (hek' to) h 100 one hundred 1x102 kilo (kil' o) k* 1 000 one thousand 1x103 mega (meg' a) M* 1 000 000 one million 1x106 giga (ji' ga) G 1 000 000 000 one thousand million 1x109 tera (ter' a) T 1 000 000 000 000 one-million million 1x1012 ------------------------------------------------------------------------- * Most commonly used. 1.3 MATHEMATICAL NOTATION (US) Mathematical Power Name ------------------------------------------------------------------------- ----- 10 18 or 1,000,000,000,000,000,000 one quintillion 10 15 or 1,000,000,000,000,000 one quadrillion 10 12 or 1,000,000,000,000 one trillion 10 9 or 1,000,000,000 one billion 10 6 or 1,000,000 one million 10 3 or 1,000 one thousand 10 2 or 100 one hundred 10 1 or 10 ten 10 0 or 1 one 10 -1 or 0.1 one tenth 10 -2 or 0.01 one hundredth 10 -3 or 0.001 one thousandth 10 -6 or 0.000 001 one millionth 10 -9 or 0.000 000 001 one billionth 10 -12 or 0.000 000 000 001 one trillionth 10 -15 or 0.000 000 000 000 001 one quadrillionth 10 -18 or 0.000 000 000 000 000 001 one quintillionth ------------------------------------------------------------------------- 1.4 DIFFERENT PREFIX DESIGNATION ------------------------------------------------------------------------- Designation USA & French Power British & German Power ------------------------------------------------------------------------- million 1000 thousands 10 6 1000 thousands 10 6 milliard 1000 millions 10 9 1000 millions 10 9 billion 1000 millions 10 9 1 million millions 10 12 trillion 1000 billions 10 12 1 million billions 10 18 (a million millions) quadrillion 1000 trillions 10 15 1 million trillion 10 24 quintillion 1000 quadrillions 10 18 a million quadrillion 10 30 ------------------------------------------------------------------------- 1.5 ROMAN NUMERALS ------------------------------------------------------------------------- I = 1 II = 2 III = 3 IV = 4 V = 5 VI = 6 VII = 7 VII = 8 IX = 9 X = 10 XI = 11 XII = 12 XIII = 13 XIV = 14 XV = 15 XVI = 16 XVII = 17 XVIII = 18 XIX = 19 XXX = 30 XL = 40 L = 50 LX = 60 LXX = 70 LXXX = 80 XC = 90 C = 100 CC = 200 CCC = 300 CD = 400 D = 500 DC = 600 DCC = 700 CCC = 800 CM = 900 M = 1000 MM = 2000 MMM = 3000 ------------------------------------------------------------------------- 1.6 METRIC INTERRELATIONSHIPS Conversions from a multiple or sub-multiple to the basic units of meters, liters, or grams can be done using the table. For example, to convert from kilometers to meters, multiply by 1,000 (9.26 kilometers equals 9,260 meters) or to convert from meters to kilometers, multiply by 0.001 (9,260 meters equals 9.26 kilometers) Length, weight, Prefix Symbol capacity Area Volume ------------------------------------------------------------------------- exa E 10 plus-18 10 plus-36 10 plus-54 peta P 10 plus-15 10 plus-30 10 plus-45 tera T 10 plus-12 10 plus-24 10 plus-36 giga G 10 plus-9 10 plus-18 10 plus-27 mega M 10 plus-6 10 plus-12 10 plus-18 hectokilo hk 10 plus-5 10 plus-10 10 plus-15 myria ma 10 plus-4 10 plus-8 10 plus-12 kilo k 10 plus-3 10 plus-6 10 plus-9 hecto h 10 plus-2 10 plus-4 10 plus-6 deka da 10 plus-1 10 plus-2 10 plus-3 basic unit - 1 meter 1 meter2 1 meter3 1 gram 1 liter deci d 10 -1 10 -2 10 -3 centi c 10 -2 10 -4 10 -6 milli m 10 -3 10 -6 10 -9 decimilli dm 10 -4 10 -8 10 -12 centimilli cm 10 -5 10 -10 10 -15 micro u 10 -6 10 -12 10 -18 nano n 10 -9 10 -18 10 -27 pico p 10 -12 10 -24 10 -36 femto f 10 -15 10 -30 10 -45 atto a 10 -18 10 -36 10 -54 ------------------------------------------------------------------------- 2. I N T E R N A T I O N A L S Y S T E M O F U N I T S ( S I ) ========================================================================= The International System of Units is an internationally agreed system of measurement that uses seven base units, with two supplementary units. All other SI units are derived from the seven base units. In addition, multiples and sub-multiples (=fractions) of units are expressed by the use of approved affixes. BASE UNITS --------------------------------------------------------- physical quantity name symbol --------------------------------------------------------- length meter m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K luminous intensity candela cd amount of substance mole mol --------------------------------------------------------- SUPPLEMENTARY UNITS --------------------------------------------------------- physical quantity name symbol --------------------------------------------------------- plane angle radian rad solid angle steradian sr --------------------------------------------------------- 2.1 LENGTH Unit: meter -- m ------------------------------------------------------------------------- The meter is defined as 1,650,763.73 wavelengths in vacuum of the orange-red line of the spectrum of krypton-86 (kr86). The SI unit of area is the square meter (m2). Land is often measured by the hectare (10,000 square meters, or approximately 2.5 acres). The SI unit of volume is the cubic meter (m3). Fluid volume is often measured by the liter (0.001 cubic meter). 2.2 TIME Unit: second -- s ------------------------------------------------------------------------- The second is defined as the duration of 9,192,631,770 cycles of the radiation associated with a specified transition of the cesium atom. It is realized by turning oscillator to the resonance frequency of the cesium atoms as they pass through a system of magnets and a resonant cavity into a detector. The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz equals a cycle per second. Dividing distance by time give speed. The SI unit for speed is the meter per second (m/s), approximately 3 feet per second. Rate of change in speed is called acceleration. The SI unit for acceleration is the meter per second per second (m/s2). 2.3 MASS Unit: Kilogram -- kg. ------------------------------------------------------------------------- The standard for the unit of mass, the kilogram, is a cylinder of platinum-iridium alloy kept by the International Bureau of Weights and Measures at Paris, France. There is a duplicate at the National Bureau of Standards in the United States. This is the only base unit still defined by an artifact. Closely allied to the concept of mass is that of force. The SI unit of force is the newton (N). A force of 1 newton, when applied for 1 second, will give to a 1 kilogram mass a speed of 1 meter per second (an acceleration of 1 meter per second per second). 1kg. 1m 1N = ------- 1s2 One newton equals approximately two tenth of a pound of force. The weight of an object is the force exerted on it by gravity. Gravity gives a mass a downward acceleration of about 9.8 m/s2. The SI unit for work and energy of any kind is the joule (J). 1J = 1N . 1m The SI unit for power of any kind is the watt (W). 1J 1W = -- 1s 2.4 TEMPERATURE Unit: Kelvin -- K ------------------------------------------------------------------------- The thermodynamic or Kelvin scale of temperature used in SI has its origin or zero point at absolute zero and has a fixed point at the triple point of water defined as 273.16 kelvins. The Celsius scale is derived from the Kelvin scale. The triple point is defined as 0.01°C on the Celsius scale, which is approximately 32.02°F on the Fahrenheit scale. The relationship of the Kelvin, Celsius, and Fahrenheit temperature scales is shown below. ------------------------------------------------------------ Kelvin Celsius Fahrenheit ------------------------------------------------------------ Water Boils 373.15 100 212 Body 310.15 37 98.6 Temperature Water Freezes 273.15 0 32 Freezing 233.13 -40 -40 Absolute Zero 0 -273.15 -459.67 ------------------------------------------------------------ Temp F + 40 = 1.8 (Temp C + 40) Temp F = 1.8 (Temp C) + 32 = 1.8 (Temp K)
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