Units

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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.

Contents

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 Available_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 yr
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
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