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A value in decimal degrees to 5 decimal places is precise to 1.11 metres (3 ft 8 in) at the equator. Elevation also introduces a small error: at 6,378 metres (20,925 ft) elevation, the radius and surface distance is increased by 0.001 or 0.1%.
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [ 4 ] It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit . [ 5 ]
Minutes and seconds need not be specified. If no degrees are specified then a value of zero is assumed. This template does not attempt to trap invalid values and results in this case might be undefined. The decimal precision of the result is determined by the value assigned rnd, which defaults to 7.
The value of π as used by the Greek mathematician and scientist Ptolemy was 3;8,30 = 3 + 8 / 60 + 30 / 60 2 = 377 / 120 ≈ 3.141 666.... [28] Jamshīd al-Kāshī , a 15th-century Persian mathematician, calculated 2 π as a sexagesimal expression to its correct value when rounded to nine subdigits (thus to 1 / 60 9 ...
degrees and decimal minutes: 40° 26.767′ N 79° 58.933′ W; decimal degrees: +40.446 -79.982; There are 60 minutes in a degree and 60 seconds in a minute. Therefore, to convert from a degrees minutes seconds format to a decimal degrees format, one may use the formula
For higher precision, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, and parts of a minute are expressed in decimal notation, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E.
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [ 1 ] In the table below, the label "Undefined" represents a ratio 1 : 0. {\displaystyle 1:0.}
Signed binary angle measurement. Black is traditional degrees representation, green is a BAM as a decimal number and red is hexadecimal 32-bit BAM. In this figure the 32-bit binary integers are interpreted as signed binary fixed-point values with scaling factor 2 −31, representing fractions between −1.0 (inclusive) and +1.0 (exclusive).