Geometry of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 27

39.58, - 105.64, again adding it to the map notes. How far is this point from
the summit of the mountain? In what direction is this point from the summit
of the mountain, and why? Remove one more digit and search for 39.5, - 105.6,
again adding it to the map notes. How far is this point from the summit of the
mountain? In what direction is this point from the summit of the mountain,
and why? Finally, remove one more digit and search for 39, - 105, again adding
it to the map notes. How far is this point from the summit of the mountain? In
what direction is this point from the summit of the mountain, and why? The
points should be getting gradually farther from the mountain peak, because
you are removing significant digits from the coordinate pair.
Examine all five of your points. In what “direction” did the points “move” as
you cut significant digits off of your values? The points move to the south and
to the east, toward the origin of the Cartesian coordinate System, which on
the Earth is 0,0, or in the Atlantic Ocean off the coast of western Africa. In
what direction will your points move if you round up to the next significant
digit? Test your answers on your map. The points will move north and west if
you round “up” to the next digit.
Why, then, is keeping significant digits to the right of the decimal point impor-
tant when you are mapping your data? This is important because a loss of even
one significant digit changes the location of any mapped point. Figure 1.17
illustrates this situation in which the hundredths decimal place is dropped.
Figure 1.17 Dropping the hundredths decimal place makes a noticeable difference in
geographic location.