# 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 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