# 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)

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 hourspeed 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 pounds210 [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