Units

International System of Units from NIST

  Length: meter Requires definition of second and uses fixed speed of light (based on attribute of universe as we understand it)
  Mass: kilogram The standard is an actual physical object  (human definition)
  Time: second Based on frequency of light from an atomic transition (attribute of universe)
  Electric current: ampere Related electrical characterics of an electron to mechanical concept of force
 Temperature: kelvin
 Based on the property of water, a fundamental substance - combination of temperature and pressure at which water is a solid, liquid and a gas. (Triple point of water)
 Substance: mole
 Chemistry/physics.  A mole of C14 has a mass of 0.012 kg. One mole is approximately 6.022 x 1023 atoms (mole)
From Wikipedia:

Moles of everyday entities

Note: all of the following are accurate to approximately one significant figure.

  • Given that the volume of a grain of sand is approximately 10-12 m3[8], and given that the area of the United States is about 1013 m2[9], it therefore follows that a mole of sand grains would cover the United States in approximately one centimeter of sand.
  • A human body contains very roughly one hundred trillion cells[10]; there are roughly six billion people on Earth; so the total number of human cells on the planet is approximately 100×1012*6×109=6×1023, which is very close to one mole.
  • Since the Earth has a radius of about 6400 km[11], its volume is approximately 1021 m3. Since about 500 large grapefruit will fit in one cubic meter[12], it therefore follows that a mole of grapefruit would have approximately the same volume as the Earth.
 Luminosity: candela
 


Base units from NIST - National Institute of Science and Technology

  
Table 1.  SI base units

SI base unit
Base quantity Name Symbol
length meter m
mass kilogram       kg
time second s
electric current ampere A
thermodynamic temperature       kelvin K
amount of substance mole mol
luminous intensity candela cd


 
Other units can be derived from these base units
Derived quantity Name Symbol
area square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared   m/s2
wave number reciprocal meter m-1
mass density kilogram per cubic meter kg/m3
specific volume cubic meter per kilogram m3/kg
current density ampere per square meter A/m2
magnetic field strength   ampere per meter A/m
amount-of-substance concentration mole per cubic meter mol/m3
luminance candela per square meter cd/m2
mass fraction kilogram per kilogram, which may be represented by the number 1 kg/kg = 1

 
Derived quantity Name Symbol   Expression  
in terms of  
other SI units		 Expression
in terms of
SI base units
plane angle radian (a) rad   - m·m-1 = 1 (b)
solid angle steradian (a) sr (c)   - m2·m-2 = 1 (b)
frequency hertz Hz   - s-1
force newton N   - m·kg·s-2
pressure, stress pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat   joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric charge, quantity of electricity coulomb C   - s·A
electric potential difference,
electromotive force		 volt V W/A m2·kg·s-3·A-1
capacitance farad F C/V m-2·kg-1·s4·A2
electric resistance ohm Omega V/A m2·kg·s-3·A-2
electric conductance siemens S A/V m-2·kg-1·s3·A2
magnetic flux weber Wb V·s m2·kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2·kg·s-2·A-2
Celsius temperature degree Celsius °C   - K
luminous flux lumen lm cd·sr (c) m2·m-2·cd = cd
illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd
activity (of a radionuclide) becquerel Bq   - s-1
absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2·s-2
dose equivalent (d) sievert Sv J/kg m2·s-2
catalytic activity katal kat
s-1·mol
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

Sizes

Table 5.  SI prefixes
Factor Name  Symbol
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 deka da
 
Factor Name  Symbol
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

Scientific notation - powers of 10

 Scientific notation
a\,\times\,10^b\!     - b is the exponent, a is the mantissa  - On calculators and computers this may be written as aEb, e.g., 1.25E+01
    Why?   We need a wide range of numbers to describe the universe, e.g.,