Geology Reference
In-Depth Information
Note that this is not 20/180, which would be dividing
by the final, not the original, amount. Dividing by the
final amount to determine a percent change is a com-
mon error that must be avoided.
As another example, we might ask for a discount
of 10% on the price of some quartz crystals that we
need for our collection. How would we calculate it?
and the length or distance between the two points.
Both of these quantities can be obtained from a topo-
graphic map. Then the relationship of the "rise"
divided by the "run" is used to calculate slope. Let's
use the data in Figure 3.1 to determine the slope
between points A and B, both on contour lines, on a
hillslope.
The difference in elevation between A and B is
400 meters obtained from the contour lines
(900m - 500m = 400m); the horizontal distance is 2
kilometers, obtained by comparison with the scale for
the map. The gradient or slope is a fraction that gives
the rate of change from A to B and is determined by:
10% of $200 = (10/100)
X
$200 = $20
which is the amount the price would be lowered, that
is, $200 - $20. The new, discounted price is $180.
rise (vertical change)
400 meters
400m
Remember the following.
run (horizontal dist.)
_ 1
~ 5
2 kilometers
2000m
1.
When determining percent, you are taking a fraction
of 100 (per cent, from the Latin, centum [hundred] and
means out of 100).
0.2
That is, there is a lm drop for every 5m of horizontal
distance or 0.2 m in 1 meter on the map. The units
(meters) cancel, making the slope dimensionless. We
can think of this as a slope of lm drop in 5m of hori-
zontal distance. We can convert the ratio of 0.2 to a
percent by multiplying as follows (remember that
0.2 = 2/10):
2.
When determining percentage increase or decrease
in a quantity, use the amount of change to construct
the numerator (top) of the fraction and the amount
you are comparing to (the original amount) as the
denominator (bottom) of the fraction.
0.2
X
100% = 2/10
X
100% = 20%
Slope or Gradient
The slope of the land surface or a river is often of inter-
est in the study of Earth. It is often inadequate to char-
acterize a slope as "steep" or "gentle," more precision
is needed. Slope is calculated by using the difference in
elevation between two points (either a rise or a drop if
we were traversing from one point to the other point)
Sometimes slope is expressed in the units actually
measured on the map. For example, there might be a
drop of 150 feet in the elevation of a road between the
center of the city and the river's edge over a distance
of 3 miles. The slope or gradient could be expressed in
feet/mile as follows:
map view
FIGURE 3.1
Map view (left) and profile (right) showing the relative position of Points A and B for gradient determination.
