What Are the Prefixes(2)

8/8/2019 What Are the Prefixes(2)

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What Are The Prefixes?The following two tables show the most commonly used prefixes for S.I.base units.Firstly, we have prefixes that talk about multiples of a unit (i.e. more thanone)...

Multiple Prefix Abbreviation

10 deca da10^2 = 100 hecto h

10^3 = 1000 kilo k

10^6 mega M

10^9 giga G

10^12 tera T

... and now we have the prefixes corresponding to fractions of a whole

unit ...Fraction Prefix Abbreviation

10^-1 = 1/10 deci d

10^-2 = 1/100 centi c

10^-3 = 1/1000 milli m

10^-6 micro

10^-9 nano n

10^-12 pico p10^-15 femto f

10^-18 atto a

NOTES:1. A notation like 10^6 means 10 raised to power 6, or a "1" followedby six "0"s (i.e. 10^6=1000000). We represent it this way becauseunfortunately superscripts are not possible in this program.2. It is important not just to get an abbreviation's letter(s) correct, butalso to have it in the proper case (upper- or lower-case). There is a big

difference between 1 mm and 1 Mm!3. The abbreviation for the prefix "micro" ( ) is the Greek letter mu.4. Finally, notice how, except for the first couple of entries in eachtable, the prefixes increase (or decrease) by multiples of 1000.Historically, it has been found that this keeps measurements to amanagable number of digits. For example, it is easy to tell the size of475.1 grams. However, to the nearest 1000, how big is 12650384? Noticehow you had to count the digits carefully? It could have been easier if Iwrote this number as 12650.384 x 10^3. Then you can quickly see that it

is closest to 12 650 lots of one thousand.

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somewhere in the world there is a block of mass that the internationalscientific community had agreed weighs exactlyone kilogram. Everyother weight is measured relative to this prototype. Consequently, ifsomebody dropped the prototype and a little bit fell off, everything elsewould weigh a little bit more (in kilograms), since the definition of akilogram would be a smaller mass.

The triple point of waterthat is mentioned in the definiton of thekelvin, is the temperature at which ice, liquid water and steam can allexist simultaneously. You may recognise this by its more familiartemperature of zero degrees Celsius. The steridian that is mentioned in the definition of the candela is athree-dimensional analogue of an angle. In effect, if we take a sphere ofunit radius, then a segment of one steridian covers one quarter of thesurface area of the sphere.

The S.I. Base UnitsThe unit of measurement for any physical quantity is derived from acombination of the seven base units. These base units are:1. metre (m) -- length2. kilogram (kg) -- mass3. second (s) -- time4. ampere (A) -- amount of electric current5. kelvin (K) -- temperature6. candela (cd) -- brightness (of light)7. mole (mol) -- amount of (chemical) substanceEach of these units is carefully defined and all other measurements are inrelation to these definitions (or standards). The page about standardsshows how these definitions are made.A guiding principle of the S.I. units is that new units can be formed fromthe base units to avoid unnecessarily large or small numbers. This is donethrough the use ofprefixes, which is the subject of the next page.

Other Units In Common UseApart from the SI units we have discussed so far, there are some other

units in common usage. These are so well-known thatthey are often usedin place of the appropriate SI unit. Sometimes they are simply morepractical (for example, we don't measure temperature in kelvins, sinceusing degrees celsius leads to smaller numbers), or they may simply bethe historical units in a specialised field.

Some examples of common (non-SI) units

UnitsAbbr.

Used tomeasure .

..

Notes

tonne t mass / 1 tonne = 1000 kg

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stonepoundounce

stlboz

weightNot to be confused with the ton which is2240 pounds1 lb = 2.2 kg

atmospheremillimetreof mercurymillibar

atmmm

Hgmb

pressure1 atm = 10^5 Pa (* see note below)1 atm = 76 mm Hg1 mb = 100 Pa (a meteorological unit)

litrecupteaspoon

L

tspn

volume(capacity)

1 L = 10^(-3) m^31 cup = 250 mL1 tspn = 5 mL

degreeCelsius

Ctemperature

0 C = 273.16 KA change of one degree Celsius is equalto a change of one kelvin.

Nauticalmile

nmile

distance 1 n mile = 1.852 km

kilometresper hourthe knot

k/h(kph)kn

velocityMore common than m/s1 kn = 1 n mile / h

hectare ha area 1 ha = 10 000 m^2

kilowatt

hour kW energy 1 kW h = 3.60 MJ (* see note below)

minutehourdayyear

minh

timeThese are useful multiples of the second.Our system of time is based on multiplesof 60 for historical reasons only.

Notes Pa is the abbreviation for Pascal, which is the SI unit for pressure.One Pascal is one newton per square metre (1 Pa = 1 N/m^2). The

newton (N) is itself a shorthand notation for the SI unit of force.1 N = 1 kg m/s^2, is the force required to accelerate a mass of onekilogram at a rate of one metre per second every second. J is the abbreviation forJoule, a unit of energy or work. One joule isthe amount of work required to apply a force of one newton over adistance of one metre. In other words, 1 J = 1 Nm = kg m^2/s^2. Thewatt (W) is an older measure of energy and does not convert so nicely toSI units (i.e. there is a conversion factor involved). Some of these units (such as minutes) are part of the metric system,

however they are not SI units, as they are not derived from base unitsmultiplied by powers of ten.

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SI Prefixes

Number

Prefix

Symbol

10 1deka-

da

10 2 hecto-

h

10 3 kilo- k

10 6mega-

M

10 9 giga- G

10 12 tera- T

10 15 peta- P

10 18 exa- E

10 21 zeta- Z

10 24yotta-

Y

Number

Prefix

Symbol

10 -1 deci- d

10 -2centi

-c

10 -3 milli- m

10 -6micro-

10 -9nano-

n

10 -12 pico- p

10 -15femto-

f

10 -18 atto- a

10 -21zepto-

z

10 -24yocto-

y

"I have three?Numbers are meaningless without the correct units!

Dimension is an abstract quality of measurement without scale (e.g.length).A unit is a number which specifies a previously agreed scale (e.g.metres).

There are four fundamental dimensions: length time mass

electric charge

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The Systeme International d'Unites (SI) (1960) is based uponseven principal units:

Category:Name:

Abbreviation:

Definition:

Length metre mThe distance light travels in a vacuum in1/299792458 of a second.

Masskilogram

kgThe mass of an international prototype inthe form of a platinum-iridium cylinderkept at Sevres in France.

Timesecond

sThe time taken for 9192631770 periods ofvibration of the caesium-133 atom tooccur.

Electriccurrent ampere A

The current which produces a specified

force between two parallel wires whichare 1 metre apart in a vacuum.

Temperature

kelvinK(not K)

1/273.16 of the thermodynamictemperature of the triple point of water.

Amount ofsubstance

mole molThe amount of substance that contains asmany elementary units as there areatoms in 0.012 kg of carbon-12.

Luminousintensity

candela

cdThe intensity of a source of light of aspecified frequency, which gives aspecified amount of power in a givendirection.

Derived S.I. Units:Many other units are derived from the 7 principal SI units, e.g:farad [F]

The SI unit of the capacitance of an electrical system, i.e. its capacity to

store electricity. This is a large unit as defined and is often used as amicrofarad [F]. (Michael Faraday, 1791-1867)hertz [Hz]

The SI unit of the frequency of a periodic phenomenon. One hertzindicates that 1 cycle of the phenomenon occurs every second. Higherfrequencies such as the kilohertz [kHz] and megahertz [MHz] arecommonly used. (Heinrich Rudolph Hertz, 1857-94)joule [J]The SI unit of work or energy. One joule is the amount of work done when

an applied force of 1 newton moves through a distance of 1 metre in thedirection of the force. (James Prescott Joule, 1818-89)

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Newton [N]The SI unit of force. One Newton is the force required to give a mass of 1kilogram an acceleration of 1 metre per second per second. (IsaacNewton, 1642-1727)ohm [W]

The SI unit of resistance of an electrical conductor. Its symbol is the Greek

letter known as 'omega' (W). (Georg Simon Ohm, 1789-1854)pascal [Pa]The SI unit of pressure. One Pascal is the pressure generated by a force of1 Newton acting on an area of 1 square metre. A small unit, often usedas the kilopascal [kPa]. (Blaise Pascal, 1623-62)siemen [S]

The SI unit of conductance. One siemen is the conductance at which apotential of 1 volt causes a current of 1 ampere to flow. Often expressedas microsiemen [S] for aqueous solutions. (Named after ???)volt [V]

The SI unit of electric potential. One volt is the difference of potentialbetween two points of an electrical conductor when a current of 1ampere flowing between those points dissipates a power of 1 watt.(Count Alessandro Giuseppe Anastasio Volta, 1745-1827)watt [W]

The unit used to measure power or the rate of doing work. One watt is apower of 1joule per second. (James Watt, 1736-1819)

S.I. Prefixes:S.I. units can be made bigger or smaller by the use of appropriateprefixes, for example: The farad is a rather large unit for most uses, so 1*10-6 F = 1microfarad (1 F) is commonly used. 1*103 Hz = 1 kilohertz [1 kHz] and 1*106 Hz = 1 megahertz [1 MHz]. The watt is a small unit, generally used in terms of 1000 watts at atime = 1 kilowatt [1 kW]. 1*106 watts = 1 megawatt [MW] and 1*109

watts = 1 gigawatt [GW].

Name: Symbol: Size: Factor:

yotta Y 1 000 000 000 000 000 000 000 000 10 24

zetta Z 1 000 000 000 000 000 000 000 10 21

exa E 1 000 000 000 000 000 000 10 18

peta P 1 000 000 000 000 000 10 15

tera T 1 000 000 000 000 10 12

giga G 1 000 000 000 10 9

mega M 1 000 000 10 6

kilo k 1 000 10 3

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http://www.newton.cam.ac.uk/newtlife.htmlhttp://www.newton.cam.ac.uk/newtlife.htmlhttp://www.theelevatormuseum.org/e/e-11.htmhttp://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.htmlhttp://www.italian-american.com/volta.htmhttp://www.spartacus.schoolnet.co.uk/SCwatt.htmhttp://www.newton.cam.ac.uk/newtlife.htmlhttp://www.newton.cam.ac.uk/newtlife.htmlhttp://www.theelevatormuseum.org/e/e-11.htmhttp://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.htmlhttp://www.italian-american.com/volta.htmhttp://www.spartacus.schoolnet.co.uk/SCwatt.htm


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hecto h 100 10 2

deca da 10 10 1

1

deci d 0.1 10 -1

centi c 0.01 10 -2

milli m 0.001 10 -3

micro 0.000 001 10 -6

nano n 0.000 000 001 10 -9

pico p 0.000 000 000 001 10 -12

femto f 0.000 000 000 000 001 10 -15

atto a 0.000 000 000 000 000 001 10 -18

zepto z 0.000 000 000 000 000 000 001 10 -21

yocto y 0.000 000 000 000 000 000 000 001 10 -24

Usage: Many units are eponymous, i.e. named after people who wereprominent in early work done within the field in which the unit is used. A unit which is named after a person is written in lower case(newton, volt, pascal etc.) when named in full, but should start with acapital letter (N, V, Pa, etc.) when abbreviated. The unit or abbreviation should be separated from the number towhich it refers by a space, e.g. "99 F", not "99F". Unit abbreviations (such as J, N, g, Pa, etc.) are NEVER followed by afull-stop unless at the end of a sentence. Units written in abbreviated form are NEVER pluralised. To make numbers easier to read they may be divided into groups of3 separated by spaces (or half-spaces) but NOT commas. Any unit may take only ONE prefix. For example "millimillimetre"should be written as "micrometre" (m).Why do we need S.I. units?

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S.I. Units make it easy to convert from one scale toanother, e.g:If x = 1 m, volume of cube = 1 * 1 * 1 = 1 m3

Since 1 m = 100 cm, volume of cube = 100 * 100 *100 = 1*106 cm3and 1 m = 1*106 m, volume of cube = 1*106 *1*106 * 1*106 = 1*1018 m3Therefore, 1 cm3 = 1*1012 m3, etc.

Centigrade and Celsius:The Centigrade (from the Latin centum, "a hundred", plus gradus,"degree") scale of temperature (1801) is defined as "a thermometricscale on which the interval between the freezing point of water and theboiling point of water is divided into 100 degrees with 0 representing thefreezing point and 100 the boiling point".

This has now been replaced by the Celsius scale (named after AndersCelsius, 1701-1744), "an international thermometric scale on which theinterval between the triple point * of water and the boiling point of wateris divided into 99.99 degrees with 0.01 representing the triple point and100 the boiling point".* The triple point of water is the condition of temperature and pressureunder which the gaseous, liquid, and solid phases of a substance canexist in equilibrium.However, the S.I. unit of temperature is the Kelvin:Example:K = 273 + C25C = 273 + 25 = 298 K

Work and energyEnergy is the ability of a system to perform work(the transfer of energy

from one system to another).Power is the rate at which work is done, i.e. the amount of work per unittime.Force is an action which maintains or alters the position of a body, ordistorts it. Because force has both magnitude and direction, it is known asa vector quantity.

The mass of an object is a measure of the object's resistance to changesin either the speed or direction. Weight and mass are not the same thing!

The weight of an object is the force it exerts under a given gravitational

force. Thus the weight of an astronaut is different on the moon than on

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glass 0.75 metres from the bar to your mouth? The force exerted by theglass due to gravity is given by the equation:force = mass * acceleration, so in this case:force = mass * acceleration due to gravity= 0.675 kg * 9.8 m s-2 = 6.615 NWork = force * distance (J = N * m), so:

6.615 N * 0.75 m = 4.96 JKinetic energy is the energy of motion. An object which is in motion haskinetic energy.Kinetic energy = 0.5 * mass * velocity2

Example:What is the kinetic energy of an 85 kg man running at 4.25 m-2 ?0.5(85 * 4.252) = 768 JWhat is his kinetic energy if he sprints at 8.9 m-2 ?0.5(85 * 8.92) = 3366 JNote that kinetic energy is directly proportional to the mass of the movingobject, but proportional to the square of its speed, e.g. as speed doubles,kinetic energy increases four-fold, but tripling the speed increases theenergy nine-fold! That's why high speed car crashes are so dangerous!Potential energy is the energy stored in an object as the result of itsposition. The main sources of potential energy are elastic potential (as inbent branches and bows and arrows) and gravitational potential (as infalling down stairs).Potential energy = mass * gravity * height (defined with respect to anarbitrary zero height)

There is a direct relationship between stored gravitational potential andthe height which an object falls - as you will know if an apple falls on yourhead from five metres compared with one metre!

Electricity:Ohm's Law states that:The potential difference (voltage) across an ideal conductor isproportional to the current through it.

The constant of proportionality is called the "resistance", R.

Ohm's Law is given by:V = I * RAlternatively:I = V/RR = V/Iwhere V is the potential difference between two points which include aresistance R and I is the current flowing through the resistance.Electrical power (in watts, W) = V * IIn biology, conductance is often quoted, S = 1/R; i.e. the ability of a

solution to allow an electric current to flow through it; the reciprocal of

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resistance. Conductance (or conductivity) is usually expressed asmicrosiemens per cm (S cm-1).Example:A water sample from a lake has a resistance of 6666 W cm-1.What is its conductivity?S = 1/R

S = 1/6666 = 1.5*10

-4

= 150 S cm

-1

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Mathematical constants, Prefixes and Suffixespi = 3.1415926536e = 2.7182818284log e = 0.434294ln 10 = 2.302591 radian = 57.2958 degrees or 57 degrees 17 minutes 45seconds

log 2 = 0.301029995664log 3 = 0.47712125471log 7 = 0.84509804

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I = 1II = 2III = 3IV = 4V = 5X = 10

L = 50C = 100D = 500M = 1000

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What Are the Prefixes(2)