Geography Reference
In-Depth Information
precision, and is frequently required in GIS. With regular “real” numbers, called floating-point, you can
count on six significant digits. With double-precision numbers you can count on 16 significant digits.
Scientific Notation, Numerical Significance,
Accuracy, and Precision
How Old Is the Dinosaur?
The curator of a natural history museum had a habit, from time to time, of walking around and listening to the
guides give their lectures at the various exhibits. One day he arrived just in time to hear that the museum's
Tyrannosaurus rex was sixty-five million and three years old. He went back to his office and told his secretary:
“Gladys, tell George I want to see him as soon as he's done with his tour.” When George appeared, the curator
exasperatedly asked him, “What do you mean telling people that the Tyrannosaurus rex fossil is sixty-five million
and three years old?” George looked abashed, but said confidentially, “Well, you hired me three years ago and you
told me then that the skeleton was sixty-five million years old, so . . .”
A GIS will deal with very precise numbers—that is, numbers that contain many digits. For example,
locating the longitude of a point on Earth's surface within a centimeter (not at all an unrealistic
expectation nowadays) requires a number with 10 significant digits—for example, 123.4567890. Because
of the number of bits devoted to “ordinary” numbers by most computers, and because fractional decimal
numbers may not be represented exactly by fractional binary numbers, GIS frequently use “double-
precision” numbers to represent positions.
Also, a GIS may deal with very big and very small numbers. Very large and very small numbers are
stored in the computer in a fashion similar to scientific notation: The number is represented as a mantissa
(which contains the significant digits of the number) and an exponent (which tells how many digits and
in which direction to move the decimal point). For example, the number in scientific notation:
2.0 x 10
-7
(which is two times ten raised to the negative seventh power) represents the number
0.0000002
To use this mantissa-exponent notation to represent 7,009,181,222 you would write the following:
4
7.009181222 x 10
9
Precision vs. Accuracy
The terms “accuracy” and “precision” do not refer to the same idea. Both are important to GIS. A classic
example of the difference follows:
Weather forecaster A indicates that it will be between 40 and 50 degrees tomorrow at 4 p.m. The actual
reading turns out to be 43. Thus, the forecast was accurate, but not very precise. Forecaster A provided a
true statement but without much detail. Forecaster B states that it will be 52.47 degrees at 4 p.m. tomor-
row. The temperature turns out to be 43 degrees. Forecaster B was very precise, but not accurate.
4
The estimated world's human population as of Wednesday 25 April 2012 at 00:23 UTC (Greenwich Mean Time
(GMT)).
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