Correct use of a calculator: (a) Calculate 74658/
53222+97554 on a calculator.
[Self-check: The most common mistake results in 97555.40.]
(b) Which would be more like the price of a TV, and which would
be more like the price of a house, $3.5 × 105 or $3.55?
Compute the following things. If they don't make sense because
of units, say so.
(a) 3 cm + 5 cm
(b) 1.11 m + 22 cm
(c) 120 miles + 2.0 hours
(d) 120 miles / 2.0 hours
Your backyard has brick walls on both ends. You measure a
distance of 23.4 m from the inside of one wall to the inside of the
other. Each wall is 29.4 cm thick. How far is it from the outside
of one wall to the outside of the other? Pay attention to significant
The speed of light is 3.0 × 108 m/s. Convert this to furlongs
per fortnight. A furlong is 220 yards, and a fortnight is 14 days. An
inch is 2.54 cm.
Express each of the following quantities in micrograms:
(a) 10 mg, (b) 104 g, (c) 10 kg, (d) 100 × 103 g, (e) 1000 ng.
Convert 134 mg to units of kg, writing your answer in scientific
Solution, p. 275
In the last century, the average age of the onset of puberty for
girls has decreased by several years. Urban folklore has it that this
is because of hormones fed to beef cattle, but it is more likely to be
because modern girls have more body fat on the average and possibly
because of estrogen-mimicking chemicals in the environment
from the breakdown of pesticides. A hamburger from a hormoneimplanted
steer has about 0.2 ng of estrogen (about double the
amount of natural beef). A serving of peas contains about 300
ng of estrogen. An adult woman produces about 0.5 mg of estrogen
per day (note the different unit!). (a) How many hamburgers would
a girl have to eat in one day to consume as much estrogen as an
adult woman's daily production? (b) How many servings of peas?
The usual definition of the mean (average) of two numbers a
and b is (a+b)/2. This is called the arithmetic mean. The geometric
mean, however, is defined as (ab)1/2 (i.e., the square root of ab). For
the sake of definiteness, let's say both numbers have units of mass.
(a) Compute the arithmetic mean of two numbers that have units
of grams. Then convert the numbers to units of kilograms and
recompute their mean. Is the answer consistent? (b) Do the same
for the geometric mean. (c) If a and b both have units of grams,
what should we call the units of ab? Does your answer make sense
when you take the square root? (d) Suppose someone proposes to
you a third kind of mean, called the superduper mean, defined as
(ab)1/3. Is this reasonable?
Solution, p. 275
In an article on the SARS epidemic, the May 7, 2003 New
York Times discusses conflicting estimates of the disease's incubation
period (the average time that elapses from infection to the first
symptoms). "The study estimated it to be 6.4 days. But other statistical
calculations ... showed that the incubation period could be
as long as 14.22 days." What's wrong here?
The following photo shows the corner of a bag of pretzels. What's