Converting Units
 Write the conversion as an equation: starting number (starting units) ¼ new number (new units):
 Count the number of different units in the equation. Numbers and Measurements in the Laboratory 23
 Add that many empty fractions to the lefthand side of the equation.
 Start to fill in those fractions by adding whatever units you need to cancel the old units and adding whatever units you need to make the new units appear.
 Make the fractions equal to 1 (turn them into unit fractions).
 Multiply.
Measuring Fundamental Properties
Fundamental property  Symbol for property  Dimension  SI unit  Symbol for unit 

Amount of substance  n  N  mole  mol 
Length  l, d  L  meter  m 
Mass  m  M  kilogram  kg 
Time  t, τ  T  second  sec 
Temperature  T  q  kelvin  K 
Electric current  I  A  ampere  A 
Luminous intensity  I_{v}  J  candela  cd 
Amount of a Substance
 Dimension: N.
 SI Unit: Moles (mol).
 Physical Basis: A mole is the number of atoms in 12 g of carbon12 (12C). That number is $6.02 × 1023$
Length
 Dimension: L.
 SI Unit: Meters (m).
 Physical Basis: A meter is defined as the distance that light travels in a vacuum in $1/299792458$ of a second.
Mass
 Dimension: M.
 SI Unit: Kilogram (kg).
 Physical Basis: A kilogram is based on the international prototype of kilogram.
Time
 Dimension: T.
 SI Unit: Second (sec).
 Physical Basis: A second is defined as the amount of time it takes for a cesium133 (133Cs) atom to transition between two hyperfine levels of the ground state 9,192,631,770 times.
Temperature
 Dimension: Q.
 SI Unit: Kelvin (K).
 Physical Basis: A kelvin is the fraction $1/273.16$ of the thermodynamic temperature of the triple point of water.
Converting to Kelvin:
$K = ^oC + 273$,
$K = ({^oF  32})({5/9})+273$
Converting to Celsius:
$^oC = K  273$,
$^oC = ({^oF  32})({5/9})$
Electric Current
 Dimension: A.
 SI Unit: Ampere (A).
 Physical Basis: The ampere is that constant current, which, if maintained in two straight parallel conductors of infinite length or negligible circular cross section and placed 1 m apart in a vacuum, would produce between these conductors a force equal to $({2 × 10^{−7}}) N$ per meter of length. (An ampere is the amount of current that would be produced by an electromotive force of 1 V acting through a resistance of 1 Ω.)
Luminous Intensity
 Dimension: J.
 SI Unit: Candela (cd).
 Physical Basis: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540 × 10^12$ hertz (Hz) and that has a radiant intensity in that direction of 1/683 watt (W) per steradian (sr).
Reference Tables and Equations
GREEK SYMBOLS
Greek 

Computer key 
(United States pronunciation) And some standard uses of uppercase and lowercase symbols 

A α 
alpha 
A a 
Cutoff for statistical significance 
B β 
beta 
B b 
(1 – β) is the power of a statistical test. 
Γ γ 
gamma 
G g 
Micrograms 
Δ δ 
delta 
D d 
CHANGE IN; change in 
E ɛ 
epsilon 
E e 

Z ζ 
zeta 
Z z 
(“zateah”) 
H η 
eta 
H h 
(“ateah”) Symbol for viscosity 
Θ θ 
theta 
Q q 
(“thateah”) 
I ι 
iota 
I i 

K κ 
kappa 
K k 

Λ λ 
lambda 
L l 
Microliters Symbol for wavelength 
M μ 
mu 
M m 
(“myoo”) MicroSymbol for population mean 
N ν 
nu 
N n 
Symbol for frequency 
Ξ ξ 
xi 
X x 
(“zi” or “ksigh”) 
O ο 
omicron 
O o 

Π π 
pi 
P p 
3.1416; the circumference of a circle divided by its diameter 
P ρ 
rho 
R r 
Symbol for density 
Σ σ 
sigma 
S s 
SUM; symbol for population standard deviation 
T τ 
tau 
T t 
Time constant 
Y υ 
upsilon 
U u 

Φ φ 
phi 
F f 
(“fee”) 
X χ 
chi 
C c 
(“ki”) 
Ψ ψ 
psi 
Y y 
(“sigh”) 
Ω ω 
omega 
W w 
SYMBOL FOR OHMS; symbol for angular frequency 
PREFIXES FOR UNITS
Prefix 
Abbreviation 
Multiplier 

yotta 
Y 
10^{24} 
zetta 
Z 
10^{21} 
exa 
E 
10^{18} 
peta 
P 
10^{15} 
tera 
T 
10^{12} 
giga 
G 
10^{9} 
mega 
M 
10^{6} 
kilo 
k 
10^{3} 
hecto 
h 
10^{2} 
deca 
da 
10^{1} 
deci 
d 
10^{−1} 
centi 
c 
10^{−2} 
milli 
m 
10^{−3} 
micro 
μ 
10^{−6} 
nano 
n 
10^{−9} 
pico 
p 
10^{−12} 
femto 
f 
10^{−15} 
atto 
a 
10^{−18} 
zepto 
z 
10^{−21} 
yocto 
y 
10^{−24} 
PREFIXES FOR NOMENCLATURE
Prefix 
Multiplier 

hemi 
1/2 
mono 
1 
di, bi, bis 
2 
tri, tris 
3 
tetra 
4 
penta 
5 
hexa 
6 
hepta 
7 
octa 
8 
nona 
9 
deca 
10 
SYSTÈME INTERNATIONALE UNITS: SI UNITS
Property 
Symbol for property 
Dimension 
SI unit 
Symbol for unit 
Symbol in base units 

Length 
l, d 
L 
meter 
m 
m 
Mass 
m 
M 
kilogram 
kg 
kg 
Time 
t, τ 
T 
second 
s 
s 
Electric current 
I 
A 
ampere 
A 
A 
Temperature 
T 
Θ 
kelvin 
K 
K 
Amount of substance 
n 
N 
mole 
mol 
mol 
Luminous intensity 
I_{V} 
J 
candela 
cd 
cd 
Plane angle 
α 
– 
radian 
rad 
m m^{−1} 
Solid angle 
Ω 
– 
steradian 
sr 
m^{2} m^{−2} 
Area 
A 
L^{2} 
meters squared 
m^{2} 
m^{2} 
Volume 
V 
L^{3} 
meters cubed 
m^{3} 
m^{3} 
Volume 

L^{3} 
liter 
l or L 
10^{−3} m^{3} 
Frequency 
f 
T ^{−1} 
hertz 
Hz 
s^{−1} 
Radioactivity 

T ^{−1} 
becquerel 
Bq 
s^{−1} 
Rate, speed, velocity 
U, ν 
L T ^{−1} 
meters/second 
m s^{−1} 
m s^{−1} 
Angular velocity 
ω 
T ^{−1} 
radians/second 
rad s^{−1} 
m m^{−1} s^{−1} 
Acceleration 
a 
L T ^{−2} 
meters/second squared 
m s^{−2} 
m s^{−2} 
Molarity 
M 
N L^{−3} 
mol/liter 
M 
mol 10^{3} m^{−3} 
Density 
ρ 
M L^{−3} 
kilograms/meter cubed 
kg m^{−3} 
kg m^{−3} 
Concentration 
c 
M L^{−3} 
kilograms/liter 
kg L^{−1} 
kg 10^{3} m^{−3} 
Force, weight 
F, w 
M L T^{ −2} 
newton 
N 
kg m s^{−2} 
Pressure 
p 
M L^{−1} T ^{−2} 
pascal 
Pa; N m^{−2} 
kg m^{−1} s^{−2} 
Energy, work 
E, W 
M L^{2} T ^{−2} 
joule 
J; N m 
kg m^{2} s^{−2} 
Power 
P 
M L^{2} T ^{−3} 
watt 
W; J s^{−1} 
kg m^{2} s^{−3} 
Electrical charge 
Q 
T A 
coulomb 
C 
s A 
Electrical potential 
V 
M L^{2} T ^{−3} A^{−1} 
volt 
V; W A^{−1} 
kg m^{2} s^{−3} A^{−1} 
Electrical resistance 
R, Ω 
M L^{2} T ^{−3} A^{−2} 
ohm 
Ω; V A^{−1} 
kg m^{2} s^{−3} A^{−2} 
Electrical capacitance 
C 
M^{−1} L^{−2} T ^{4} A^{2} 
farad 
F; C V^{−1} 
kg^{−1} m^{−2} s^{4} A^{2} 
Electrical field strength 

M L T ^{−3} A^{−1} 
volts/meter 
V m^{−1} 
kg m s^{−3} A^{−1} 
Inductance 

M L^{2} T ^{−2} A^{−2} 
henry 
H; Wb A^{−1} 
kg m^{2} s^{−2} A^{−2} 
Conductance 

M^{−1} L^{−2} T^{3} A^{2} 
siemen 
S; A V^{−1} 
kg^{−1} m^{−2} s^{3} A^{2} 
Flux density 

MT ^{−2} A^{−1} 
tesla 
T; Wb m^{−2} 
kg s^{−2} A^{−1} 
Magnetic flux 

M L^{2} T ^{−2} A^{−1} 
weber 
Wb, V s 
kg s^{−2} A^{−1} m^{2} 
Luminous flux 

J 
lumen 
lm; cd sr 
cd 
Illuminance 

L^{−2} J 
lux 
lx; lm m^{−2} 
m^{−2} cd 
Luminance 

L^{−2} J 
candelas/meter squared 
cd m^{−2} 
m^{−2} cd 
Heat capacity/entropy 
S 
M L^{2} T ^{−2} Θ^{−1} 
joules/kelvin 
J K^{−1} 
kg m^{2} s^{−2} K^{−1} 
Specific entropy 

L^{2} T ^{−2} Θ^{−1} 
joules/kilogram kelvin 
J kg^{−1} K^{−1} 
m^{2} s^{−2} K^{−1} 
Thermal conductivity 

M L T ^{−3} Θ^{−1} 
watts/meter kelvin 
W kg^{−1} K^{−1} 
kg m s^{−3} K^{−1} 
The seven fundamental units (SI base units) are assumed to be mutually independent; that is, none of the base units can be constructed by arranging any of the others. The fundamental units are shown in boldface letters.
OTHER UNITS
Property 
Symbol for property 
Dimensions 
Other unit 
Symbol for unit 
To convert to SI 

Plane angle 
θ, α 

degree 
° 
rad = degrees ÷ 57.3 
Mass 
m 
M 
dalton 
D 
kg = D ÷ (6.022142 × 10^{26}) 
Temperature 
T 
Θ 
degree Celsius 
°C 
K = °C + 273.15 
Temperature 
T 
Θ 
degree Fahrenheit 
°F 
K = (5/9)°F + 255.37 
Area 
A 
L^{2} 
hectare 
ha 
m^{2} = 0.0001 ha 
Volume 
V 
L^{3} 
cubic cm 
cc 
mL = cc 
Force 
F 
M L T ^{−2} 
dyne 
dyn 
N = 105 dyne 
Pressure 
p 
M L^{−1} T ^{−2} 
atmosphere 
atm 
Pa = 9.86926 × 10^{−6} atm 
Energy, work 
E, W 
M L^{2} T ^{−2} 
calorie 
cal 
J = 0.239 cal 
Energy, work 
E, W 
M L^{2} T ^{−2} 
erg 
erg 
J = 107 erg 