Units
From WeBWorK
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 [/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 |
| Misc | |
| Amperes | amp |
| Moles | mol |
| Degrees Centrigrade | degC |
| Degrees Fahrenheit | degF |
| Degrees Kelvin | degK |
| Angle degrees | deg |
| Angle radians | rad |
