Geometry of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 13

explain how this figure is calculated, but for now, the length of a degree can
help us understand the value of precision in measuring on the Earth. Given
that one degree is 111.2 km, then the length of one minute is 111.2/60, or
1.853 km, and the length of one second is 1.853/60 = 0.03089 km, or 30.89
meters (m). If any given set of coordinates is off by one second, then the dis-
tance off on the Earth's surface is just over 30 meters. And remember, this is
at the Equator: An error of one second elsewhere on the Earth's surface is a
smaller distance but still merits attention.
Let us explore these same measurements using decimal degree format instead
of degrees, minutes, seconds. If one degree is 111.2 km at the Equator, then 0.1
degree is 11.2 km, 0.01 degree is 1.2 km, 0.001 degree is 0.12 km, 0.0001 degree
is 0.012 km, or 12 meters, and 0.00001 degree is 0.0012 km, or 1.2 meters.
Therefore, four significant digits to the right of the decimal will pinpoint a loca-
tion to within 12 meters, and five significant digits to the right of the decimal
will pinpoint a location to within 1.2 meters on the Earth's surface. Therefore,
keeping all of the significant digits in any measurement is important! Earth mea-
surement is definitely not a case when numbers should be truncated or rounded.
It is important to note, however, that simply because Global Positioning
Systems (GPS) receivers and GPS apps on smartphones can provide very pre-
cise locations, coupled with Geographic Information Systems (GIS)-based
digital maps that allow for zooming into very detailed scales, one must use
caution in the confidence placed on the resulting obtained locations. A large
number of significant digits to the right of a decimal for any latitude and longi-
tude coordinate pair does not necessarily mean that the position was gathered
from equipment or a sensor with a high degree of accuracy. Precision is not
the same as accuracy. Having the significant digits may just be a capability of
your mapping software or GPS rather than an indication of the accuracy of
your measurement.
Some readers might consider the words “accuracy” and “precision” to be syn-
onyms. It is important to clarify the distinction between these words as we will
refer to it throughout this topic. “Accuracy” refers to whether measurements
taken within a system are close to an accepted value (Math Is Fun, 2012). The
closer the measurements are to an accepted value, the more accurate that
set of measurements is said to be. “Precision,” on the other hand, refers to
whether measurements taken within a system are close to each other. One
way to model the differences is by using a target, where arrows shot at a tar-
get represent measurements within a system. Figure 1.11 shows images rep-
resenting high accuracy and high precision ( Figure 1.11a ) , high accuracy but
low precision ( Figure 1.11b ) , high precision but low accuracy ( Figure 1.11c ) ,
and low accuracy and low precision ( Figure 1.11d ) . In the best of all possible
worlds, of course, one would wish for “high” in both categories. Mathematics
may offer high accuracy; science demands replication of results and therefore
high precision. This distinction is important both in terms of knowing your
hardware, such as GPS units, as well as in terms of knowing your data.