# Difference between revisions of "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).

Units need to come at the end of the answer blank . If MathQuill (the vertical math pallet on the side of the page) is being used then the unit should be preceded by a double quote -- e.g. 9.81 "m/s^2 which invokes text mode (tT) for the units. This prevents MathQuill from rewriting the units in two dimensional typeset form. Before MathQuill was in use the units had to be preceded by a space (in most cases).

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