
Modifier Use for Plane Angles, Solid Angles, and Human Health Units



For plane and solid angles, radians and steradians are dimensionalized as modified ratios of lengths, namely length/length(radius) and length^2/length(radius)^2, respectively. The symbols in parentheses are called Unit annotations. For more information see the Units,angle and Units,solid_angle help pages.


In the Simple Units environment, these differences are minimized: this is still how these units work behind the scenes, but whenever units are combined, the decision whether this succeeds or not is made while ignoring any annotations. For example, it is possible to add a unitfree quantity to an angle.



Unit Display



Unless all units are associated with symbols or abbreviations, an expression is displayed using unit names. For example, joules per kilogram is displayed as $\frac{J}{\mathrm{kg}}$, whereas joules per clove is displayed as $\frac{\mathrm{joule}}{\mathrm{clove}}$. This does not conform to the IEEE/ASTM standards, in which the latter is written as the statement joules per clove.


In Maple output, there is no separation between groups of three digits. Furthermore, in documentation, the comma is used as a separator for groups of three digits when four or more digits appear on either side of the decimal marker. The IEEE standard is to use a space separator.



Unit Conversion Factors



In table A.1 of the IEEE/ASTM standard, the floatingpoint approximations for converting degrees, grad, and mil (angle) to radians, kilometers per hour to meters per second and lamberts to candela per square meter are labeled as exact conversions. In the Units package, the exact, rational conversion rates are used.


The table indicates that an acre equals 43560 square US survey feet, a chain equals 66 US survey feet, and a rod equals 16.5 US survey feet. Because these units are not intrinsically associated with US survey units, these conversions are used for US survey acres (acre[US_survey]), US survey chains (chain[US_survey]), and US survey rods (rod[US_survey]).


In all other cases, the Units package uses either the exact conversion rate from or a floatingpoint approximation at least as accurate as that listed in table A.1 of the IEEE/ASTM standards.



