Numbers!!!

Here is how to write out the numbers from zero to ten in a couple different ways.

Arabic
Latin 0 1 2 3 4 5 6 7 8 9 10
Roman Numerals (none) I II III IV V VI VII VIII IX X
Chinese./ Japanese

check out this site to learn more about how some numbers evolved

http://www.geocities.com/rmlyra/hindi.html

distances:  http://math.ucr.edu/home/baez/distances.html

 

Definitions of Fundamental Units

Believe it or not, all we need are these five basic quantities to measure anything in the universe.  Notice that these quantities are defined in relation to one another.  This has a sort of philosophical significance.  No quantity can be defined just by itself- it needs a relation to something else.  This means that we can not build up these five entities one by one, we need to adopt them all at the same time.  Note: don't be caught off guard by the reference to "force" in the definition of the ampere; later we'll derive a definition of force using only mass and length. 

 

quantity abbreviation unit abbreviation definition
length (d) meter (m) distance traveled by light in 1/299,742,458 of one second
time (t) second (s) duration of 9,192,631,770 oscillations of a Cesium-133 nucleus
current (I) ampere (A) flow of electricity in two parallel wires 1 meter apart producing a force of 2 E-7 Newtons per meter
temperature (T) Kelvin (K) 1/273.16 of the thermodynamic temperature of the triple point of pure water.  Water at this temperature, and a pressure of  4.56 mm Hg (.006 atm), can exist in the solid, liquid and gaseous state simultaneously.
mass (m) kilogram (kg) the mass of a platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures

 

 

Circular Definitions

quantity abbreviation unit abbreviation definition uses / equations
radius R meter (m) distance from a point on a circle to its center  
circumference C meter (m) distance around a circle C = 2 p R
solid angle   steradian (str) 4p steradians in the surface area of a sphere  
angle Q radians (rad) a measure of direction relative to a fixed axis Q = arc length / R

 

Derived Quantities

Now we'll use our five fundamental quantities to derive many more.

quantity abbreviation unit abbreviation definition uses / equations
area A square meter (m2)   formulas of the area of some shapes
volume V cubic meter (m3)   formulas of the volume of some shapes
density D kilograms per meter cubed (kg/m3) mass divided by volume density = m / V
velocity v meters per second (m/s) speed v = d / t
angular velocity w radians per second (rad/s) velocity around a point or axis w = v / R
acceleration a meters per second squared (m/s2) velocity divided by time a = v / t
angular acceleration a radians per second squared (rad/s2) acceleration around a point or axis a = a / R
force F Newton (N) push or pull needed to cause a kg to accelerate by a m/s2 Newton's 2nd Law: F = ma
gravitational field g Newtons per kilogram (N/kg) the Force due to gravity acting on a one kilogram test mass F = m g
torque t Newton meter (N-m) force around a point or axis t = R F
pressure P Pascals Pa force exerted per area P = F / A
momentum p kilogram meters per second (kg-m/s) quantity of motion  p = m v
angular momentum L kilogram meter squared per second kg-m2/s momentum around a point or axis L = R p
impulse   Newton second (N-s) change in momentum Impulse = F t
energy (work) E Joule (J) ability to do work work = F d
power P Watt (w) energy per second P = E / t
charge Q Coulomb (C) amount of charge passing a point during one second I = Q / t
voltage V volt (V) energy per charge V = E / Q
resistance R Ohm (W)   Ohm's Law:  V = I R
capacitance C farad (f) the amount of charge that can be stored on a capacitor per volt C = Q / V
electric field E Newtons per Coulomb (N/C) the force acting on a positive test charge of one Coulomb F = E Q
magnetic field B Testla (T) the quantity of magnetism arising from a coil of wire with a current density of one ampere per meter B = I / d
inductance L henry (h) the voltage generated to oppose the change in current in a circuit V = - L ( I / t)
magnetic flux F weber (Wb) the total magnetic field through a given area  = B A
period T second (s) time for one oscillation  
frequency f Hertz (Hz) oscillations per second f = 1 / T
wavelength l meter (m) distance traveled by a wave during one oscillation v = l f
           

Learn more about what some of these quantities mean at the following websites:

 http://whatis.techtarget.com/definition/0,,sid9_gci551931,00.html

http://www.unc.edu/~rowlett/units/index.html

 

 

CONVERSIONS

 

metric multipliers

  bigger       smaller  
name prefix multiplier   name prefix multiplier
yotta Y 1024   deci d 10-1
zetta Z 1021   centi c 10-2
exa E 1018   milli m 10-3
peta P 1015   micro m 10-6
tera T 1012   nano n 10-9
giga G 109   pico p 10-12
mega M 106   femto f 10-15
kilo k 103   atto a 10-18
hecto h 102   zepto z 10-21
deka D 10   yocto y 10-24

 

number

unit equivalence definition system
dozen 12   English
half dozen 6 one half dozen English
score 20   English
Avogadro's Number 6.0221E23 number of atomic mass units in a gram chemistry
myriad 10,000 innumerable  
flux   number passing through a given area per time  

 

angle

unit equivalence definition system
degree   360 in a circle English
arcminute   60 in a degree English
arcsecond   60 in an arcminute English
hour   24 in a circle astronomy

 

length

unit equivalence definition system
angstrom 10-10 m 10-8 cm atomic
inch 0.0254m one common thumbnail English
foot 0.3048m 12 inches English
yard 0.9144m 3 feet English
rod 5.0292m 5.5 yards English
furlong 201.168m 660 feet English
mile 1,609.344m 5,280 feet English
light year 9.461E15m length traveled by light in one Earth year astronomy
parsec 3.082E16 m distance at which an object would have a maximum parallax angle of 1 arcsecond astronomy
       
       
       
       

area

unit equivalence definition system
acre 4046.4560m2 square 208.7 feet on a side English
township 93,239,571.97m2 36 square miles English
       
       

volume

unit equivalence definition system
liter 0.001m3 1,000 cm3 metric
teaspoon 5E-6m3 5ml cooking
tablespoon 1.5E-5m3 3 tsp cooking
cup 2.40E-4m3 16 tbsp cooking
fluid ounce 3 E-5 m3 30 ml liquid
gill 1.1832E-4m3   liquid
pint 4.7326E-4m3 4 gills liquid
quart 9.4652E-4m3 2 pints liquid
gallon 3.7861E-3m3 4 quarts liquid
peck 7.5722E-3m3 2 gallons English
bushel 0.030289m3 4 pecks English
barrel 0.11926m3 31.5 gallons English
hogshead 0.23852m3 2 barrels English
cord 3.6246m3 128 cubic feet English
       
       
       
       
       

mass

Note: Weight is really a force!!  Instead of measuring an objects mass, it is common to measures the gravitational force the object feels on the surface of the Earth- its weight.

unit equivalence definition system
dram 1.7715E-3kg   English
ounce 0.028345kg 16 drams English
pound 0.4535kg 16 ounces English
hundredweight 45.3515kg 100 pounds English
ton (short ton) 907.0295kg 2000 pounds English
metric ton (long ton) 1015.8730kg 2240 pounds metric
       
       
       
       
       

temperature

unit equivalence definition system
degree Fahrenheit [ (F-32) * (5/9) ] + 273 temperature scale in which water melts at 32 degrees and boils at 212 degrees English
degree Celsius (Centigrade) C + 273 temperature scale in which water melts at 0 degrees and boils at 100 degrees metric
       
       
       
       
       

time

unit equivalence definition system
minute      
hour      
day      
week      
month (lunar)      
year      
decade      
century      
millenium      
       
       

other

quantity unit equivalence definition system
speed miles per hour 0.4469 m/s   English
force pound 0.4469 N weight of one pound English
pressure atmosphere 1.013E5 Pa pressure from Earth's atmosphere at sea level  
pressure bar 105 Pa    
pressure mm Hg 133.290 Pa 1 atm =  760 mmHg = 14.7 lbs/inch2  
energy calorie 4.186 J amount of energy needed to heat one cm3 of water 1 degree C metric
energy BTU 1055J British Thermal Unit English
energy electron volt 1.602e-19 J energy required to give an electron a voltage of 1 volt atomic
acceleration g 9.80665 m/s2 acceleration due to gravity on the surface of the Earth  
power from light lumen 1.4641E-3 watts power given off at 556nm astronomy
illuminance (brightness of lite-up object) lux 1.4641E-3 watts/m2 lumens per square meter astronomy
luminous intensity (brightness of source) candela 1.4641E-3 watts/str lumens per steradian astronomy
power jansky 10-26 watts   astronomy
         
         
         
         

 

PHYSICAL CONSTANTS

quantity symbol value
speed of light in a vacuum c 2.99792E8 m/s
charge of an electron e -1.60218E-19 C
gravitational constant G 6.67 E-11 Nm2/kg2
planck's constant h 6.6261E-34 Js
boltzmann's constant k 1.381 E-23 J/K
mass of electron me 9.1094E-31 kg
mass of proton mp 1.67262E-27 kg
mass of neutron mn 1.67493E-27kg
permeability of space mo 4p E-7 Wb/Am
permittivity of space eo 8.8542 E -12 C2/Nm2