Three essential mathematical skills
More often than not when a search-and-rescue team finds a hiker
dead in the wilderness, it turns out that the person won a Darwin
Award by not carrying some item from a short list of essentials, such
as water and a map. There are three mathematical essentials in this
course.
- Converting units
basic technique: subsection 0.1.9, p. 28; conversion of area, vol-
ume, etc.: subsection 0.2.1, p. 34
Examples:
0.7 kg ×
103 g(^1) kg
= 700 g.
To check that we have the conversion factor the right way up (10^3
rather then 1/ 103 ), we note that the smaller unit of grams has been
compensatedfor by making the number larger.
For units like m^2 , kg/m^3 , etc., we have to raise the conversion
factor to the appropriate power:
4 m^3 ×
(
103 mm
1 m) 3
= 4× (^109) m^3 ×
mm^3
m^3
= 4× 109 mm^3
Examples with solutions — p. 47, #6; p. 51, #31
Problems you can check atlightandmatter.com/area1checker.
html— p. 47, #5; p. 47, #4; p. 47, #7; p. 51, #22; p. 52, #40
- Reasoning about ratios and proportionali-
ties
The technique is introduced in subsection 0.2.2, p. 35, in the
context of area and volume, but it applies more generally to any
relationship in which one variable depends on another raised to some
power.
Example: When a car or truck travels over a road, there is wear
and tear on the road surface, which incurs a cost. Studies show that
the cost per kilometer of travelCis given by
C=kw^4 ,wherewis the weight per axle andkis a constant. The weight per
axle is about 13 times higher for a semi-trailer than for my Honda
Fit. How many times greater is the cost imposed on the federal
government when the semi travels a given distance on an interstate
freeway?
Problems 1015