Lab Math |

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 left-hand 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 carbon-12 (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 cesium-133 (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.

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	(“zate-ah”)
H η	eta	H h	(“ate-ah”) Symbol for viscosity
Θ θ	theta	Q q	(“thate-ah”)
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”) Micro-Symbol for population mean
N ν	nu	N n	Symbol for frequency
Ξ ξ	xi	X x	(“zi” or “k-sigh”)
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	10²⁴
zetta-	Z	10²¹
exa-	E	10¹⁸
peta-	P	10¹⁵
tera-	T	10¹²
giga-	G	10⁹
mega-	M	10⁶
kilo-	k	10³
hecto-	h	10²
deca-	da	10¹
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	m² m⁻²
Area	A	L²	meters squared	m²	m²
Volume	V	L³	meters cubed	m³	m³
Volume		L³	liter	l or L	10⁻³ m³
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 10³ 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 10³ 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 L² T ⁻²	joule	J; N m	kg m² s⁻²
Power	P	M L² T ⁻³	watt	W; J s⁻¹	kg m² s⁻³
Electrical charge	Q	T A	coulomb	C	s A
Electrical potential	V	M L² T ⁻³ A⁻¹	volt	V; W A⁻¹	kg m² s⁻³ A⁻¹
Electrical resistance	R, Ω	M L² T ⁻³ A⁻²	ohm	Ω; V A⁻¹	kg m² s⁻³ A⁻²
Electrical capacitance	C	M⁻¹ L⁻² T ⁴ A²	farad	F; C V⁻¹	kg⁻¹ m⁻² s⁴ A²
Electrical field strength		M L T ⁻³ A⁻¹	volts/meter	V m⁻¹	kg m s⁻³ A⁻¹
Inductance		M L² T ⁻² A⁻²	henry	H; Wb A⁻¹	kg m² s⁻² A⁻²
Conductance		M⁻¹ L⁻² T³ A²	siemen	S; A V⁻¹	kg⁻¹ m⁻² s³ A²
Flux density		MT ⁻² A⁻¹	tesla	T; Wb m⁻²	kg s⁻² A⁻¹
Magnetic flux		M L² T ⁻² A⁻¹	weber	Wb, V s	kg s⁻² A⁻¹ m²
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 L² T ⁻² Θ⁻¹	joules/kelvin	J K⁻¹	kg m² s⁻² K⁻¹
Specific entropy		L² T ⁻² Θ⁻¹	joules/kilogram kelvin	J kg⁻¹ K⁻¹	m² 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 × 10²⁶)
Temperature	T	Θ	degree Celsius	°C	K = °C + 273.15
Temperature	T	Θ	degree Fahrenheit	°F	K = (5/9)°F + 255.37
Area	A	L²	hectare	ha	m² = 0.0001 ha
Volume	V	L³	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 L² T ⁻²	calorie	cal	J = 0.239 cal
Energy, work	E, W	M L² T ⁻²	erg	erg	J = 107 erg

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