Units

The answers you enter as the solutions to your WebWork problem sets must conform to the following conventions, in order to be interpreted and graded correctly.

Problems requiring a numerical answer

Most answers consist of a numerical value followed by an abbreviation for the appropriate units of the physical quantity. A space must separate the numerical value from the units, as in for example 1.234 m.

Numerical values

The numerical value may be written as a floating point decimal, for example 0.00314159, or in scientific notation as either 3.14159E-3 (as in FORTRAN) or 3.14159*10^-3 (with * signifying multiplication, and ^ signifying exponentiation; note in using the FORTRAN-like notation, you must use capital "E" and not small "e"). In place of a specific number for the numerical part of an answer, you may also use algebraic expressions. For example, (6+4)/2 is the same as writing 5. To see the syntax required for such expressions, as well as to see which special functions and numerical constants are recognized, see the section on [/docs/docs/pglanguage/availablefunctions.html Accepted math functions]. Note that trigonometric functions assume the argument is expressed in radians and not degrees.

Units

The units may be any compound expression of the form:

[unit]1^n1*[unit]2^n2*...*[unit]3^n3/ [unit]4^n4*[unit]5^n5*...*[unit]6^n6

where [unit]i is any of the unit abbreviations listed below, and the ni are positive or negative integers. The string of units before the / denote the numerator of the compound expression, while those following the / denote the denominator of the compound expression. There may be only one / in a given compound unit expression and no spaces are allowed within the units expression.

The abbreviations for units that are recognized by WebWork are:

abbrev.	unit name	dimension	equivalence in fundamental units
FUNDAMENTAL MKS UNITS
kg	kilograms	mass
m	meters	length
s	seconds	time
OTHER BASIC UNITS
deg	degree	angle	1 deg = pi/180 rad
rad	radian	angle	1 rad = 180/pi deg
ms	millisecond	time	1 ms = 0.001 s
min	minute	time	1 min = 60 s
hr	hour	time	1 hr = 60 min = 3600 s
day	day	time	1 day = 24 hr = 8.64E4 s
yr	year	time	1 yr = 365.25 day = 3.15576E7 s
km	kilometer	length	1 km = 1000 m
cm	centimeter	length	1 cm = 0.01 m
mm	millimeter	length	1 mm = 0.001 m
micron	micrometer	length	1 micron = 10^-6 m
um	micrometer	length	1 um = 10^-6 m
nm	nanometer	length	1 nm = 10^-9 m
A	Angstrom	length	1 A = 10^-10 m
in	inch	length	1 in = 0.0254 m
ft	feet	length	1 ft = 12 in = 0.3048 m
mi	mile	length	1 mi = 5280 ft = 1609.344 m
light-year	light year	length	1 light-year = 9.46E15 m
L	liter	volume	1 L = 10^-3 m^3
ml	milliliter	volume	1 ml = 10^-3 L = cm^3
cc	cubic centimeter	volume	1 cc = 10^-3 L = cm^3
knots	nautical miles per hour	velocity	1 knots = (1852/3600) m/s
g	gram	mass	1 g = 10^-3 kg
slug	slug	mass	1 slug = 14.6 kg
Hz	Hertz	frequency	1 Hz = 1 s^-1
kHz	kilo-Hertz	frequency	1 kHz = 1000 Hz = 10^3 s^-1
MHz	mega-Hertz	frequency	1 MHz = 10^6 Hz = 10^6 s^-1
rev	revolutions	period	1 rev = 2pi rad
cycles	cycles	period	1 cycles = 1 rev = 2pi rad
degK	degrees Kelvin	temperature
degC	degrees Centigrade	temperature
degF	degrees Fahrenheit	temperature
COMPOUND UNITS
N	Newton	force	1 N = 1 kg*m/s^2
microN	micro-Newton	force	1 microN = 10^-6 N = 10^-6 kg*m/s^2
uN	micro-Newton	force	1 uN = 10^-6 N = 10^-6 kg*m/s^2
J	Joule	energy	1 J = 1 N*m = 1 kg*m^2/s^2
kJ	kilo-Joule	energy	1 kJ = 1000 J = 10^3 kg*m^2/s^2
lbf	foot-pound	energy	1 lbf = 1.355 N*m = 1.355 kg*m^2/s^2
W	Watt	power	1 W = 1 J/s = 1 kg*m^2/s^3
kW	kilo-Watt	power	1 kW = 1000 W = 10^3 kg*m^2/s^3
dyne	dyne	force	1 dyne = 10^-5 N = 10^-5 kg*m/s^2
erg	erg	energy	1 erg= 10^-7 J = 10^-7 kg*m^2/s^2
lb	pound	force	1 lb = 4.45 N = 4.45 kg*m/s^2
ton	ton	force	1 ton = 2000 lb = 8900 kg*m/s^2
Pa	Pascal	pressure	1 Pa = 1 N/m^2 = 1 kg/m*s^2
kPa	kilo-Pascal	pressure	1 kPa = 1000 Pa = 10^3 kg/m*s^2
atm	atmosphere	pressure	1 atm = 14.7 lb/in^2 = 1.01E5 Pa = 1.01E5 kg/m*s^2
cal	calorie	energy	1 cal = 4.19 J = 4.19 kg*m^2/s^2
kcal	kilocalorie	energy	1 kcal = 1000 cal = 4190 kg*m/s^2
eV	electron volt	energy	1 eV = 1.60E-19 J = 1.60E-9 kg*m^2/s^2
kWh	kilo-Watt hour	energy	1 kWh = 3.6E6 J = 3.6E6 kg*m^2/s^2

Units Available in WeBWorK

Some WeBWorK problems ask for answers with units. Below is a list of basic units and how they need to be abbreviated in WeBWorK answers. In some problems, you may need to combine units (e.g, velocity might be in ft/s for feet per second).

Unit	Abbreviation
Time
Seconds	s
Minutes	min
Hours	hr
Days	day
Years	year
Milliseconds	ms
Distance
Feet	ft
Inches	in
Miles	mi
Meters	m
Centimeters	cm
Millimeters	mm
Kilometers	km
Angstroms	A
Light years	light-year
Mass
Grams	g
Kilograms	kg
Slugs	slug
Volume
Liters	L
Cubic Centimeters	cc
Milliliters	ml
Force
Newtons	N
Dynes	dyne
Pounds	lb
Tons	ton
Work/Energy
Joules	J
kilo Joule	kJ
ergs	erg
foot pounds	lbf
calories	cal
kilo calories	kcal
electron volts	eV
kilo Watt hours	kWh
Electric
Charge Coulombs	C
Voltage Volts	V
milivolts	mV
kilovolts	kV
megavolts	MV
Capacitance Farad	F
milifarad	mF
microfarad	uF
Resistance ohms	ohm
kilo-ohm	kohm
Misc
Amperes	amp
Moles	mol
Degrees Centrigrade	degC
Degrees Fahrenheit	degF
Degrees Kelvin	degK
Angle degrees	deg
Angle radians	rad