# Units with Scalars

To directly combine units with numbers and other units, AutoMathic requires that a few special conventions be followed.  These rules will ensure that units are unambiguously communicated, but still allow some freedom of expression.  The rules are listed here with representative examples:

Units

 Simple Unit A single word or abbreviation.  Abbreviations must NOT include periods (e.g. "ft."): e.g. mile mi Compound Unit Multiple words or abbreviations.  Depending on its context, a "compound unit" may have to be enclosed in parentheses: e.g. feet per second (miles per hour) (mi/hr) "in" as a Unit The standard abbreviation for "inch" is "in", but because "in" is also a very common word, it is only interpreted as an abbreviation for "inch" in the context of a unit (i.e. when individually enclosed in parentheses or square brackets, preceded by "unit" or "units" or "measured in" or "in terms of", immediately preceded by an open parenthesis or open bracket, or immediately followed by a close parenthesis or close bracket): e.g. (in) [in] unit in measured in in in terms of in [in/hr] [seconds/in] "has" as a Unit An abbreviation for "hectares" is "has", but because "has" is also a very common word, it is only interpreted as an abbreviation for "hectares" in the context of a unit (i.e. when individually enclosed in parentheses or square brackets, preceded by "unit" or "units" or "measured in" or "in terms of", immediately preceded by an open parenthesis or open bracket, or immediately followed by a close parenthesis or close bracket): e.g. (has) [has] unit has measured in has in terms of has [has/hr] [seconds/has]

AutoMathic's library has some common compound unit abbreviations already defined:

• MPH, KPH, FPS, MPS, MPG, and RPM.
Since their definitions already include enclosing parentheses, a predefined abbreviation of a compound unit can be treated like a "simple unit" and be used without parentheses.

Unit Phrases

Unit Phrases combine properties, scalars, and/or units into a cohesive whole that defines a measurement.  In Unit Phrases, simple or compound units can be enclosed in square brackets to simplify and shorten the unit phrase.

 Unit Phrase A "unit phrase" can be a property, followed by "measured in" or "in terms of", optionally followed by the word "unit" or "units", followed by a "unit".  If you enclose the units in square brackets, the optional word "unit" or "units" can always be omitted: e.g. speed measured in units miles per hour speed measured in [miles per hour] speed in terms of miles per hour speed in terms of [miles per hour] A "unit phrase" can be a property, followed by "in", followed by the word "unit" or "units", followed by a "unit".  If you enclose the units in square brackets, the word "unit" or "units" can be omitted: e.g. heights in unit centimeters heights in [centimeters] speed in units mi/hr speed in [mi/hr] A "unit phrase" can be a quantity, followed by the word "unit" or "units", followed by a "unit".  If you enclose the units in square brackets, the word "unit" or "units" can be omitted.  Spaces are not required around the square brackets: e.g. 210 unit pounds 210 [pounds] 210[pounds] A compound unit following a quantity must be enclosed in parentheses or square brackets, but built-in abbreviations of compound units can be treated like simple units since their definitions include enclosing parentheses. e.g. 145 unit (mi/hr) 145 [mi/hr] 145 unit mph 145[mph]

Rules-of-Thumb

Three simple rules-of-thumb for units and unit phrases are:

1. "measured in" or "in terms of" should go between a property (e.g. distance) and its unit (e.g. kilometers).  If the unit is in square brackets, the word "in" is sufficient.
• distance in terms of kilometers
• distance in [kilometers]

2. A unit following a quantity must be preceded by the word "unit" unless the unit is enclosed in square brackets.
• 5 unit miles
• 5[miles]

3. A compound unit following a quantity requires enclosing parentheses or square brackets.
• 120 unit (miles per hour)
• 120[miles per hour]

Common Usage

The "unit" and "unit phrase" building-blocks can be used in a number of ways:

• A "unit" can be used by itself.  Restricting some input to standalone units is what defines the Standalone method
• miles per hour

• A "unit phrase" can be used by itself to request a calculation
• speed in units mi/hr
• speed in [mi/hr]

• A "unit phrase" can be used in a question to ask for a measurement or conversion
• What's the speed measured in unit mi/hr?
• What's the speed in [mi/hr]?
• How many unit (mi/hr) would the speed be?
• How many [mi/hr] would the speed be?

• A "unit phrase" can be used in a statement of fact to define a measurement:
• 55 is the speed in terms of mi/hr
• 55 is the speed in [mi/hr]
• 55 unit (mi/hr) is the speed
• 55[mi/hr] is the speed

Although units are most often used in a 1-dimensional way (for example using "feet" to measure a length), units can also be used in multiple dimensions to measure things such as an area (2 dimensions), or a volume (3 dimensions).