Math
2000 - Solutions 5
Spring 2001
6a.
0.00000002 = 2 ´ 10-8 (move
the decimal point 8 places to the right).
6e.
80 billion = 80,000,000,000= 80 × 109 = 8 ´ 1010 (move the decimal point 10 places to
the left).
10d.
2.3 ´ 106 =
2,300,000 (move the decimal point 6 places to the right).
10e.
2.2 ´ 10-4 =
0.00022 (move the decimal point 4 places to the left).
12d.
In 1995 the United States contributed $1.173 ´ 109 to international organizations.
14a.
(3 ´ 104) ´ (8 ´ 105) = (3 ´ 8) ´ (104 ´ 105) = 24 ´ 109 = 2.4 ´ 1010
14e.
(8 ´ 1012) ¸ (4 ´ 109) = (8 ¸ 4) ´ (1012 ¸ 109) = 2 ´ 103
18d.
Note that 7 trillion = 7 ´ 1012 and 7
thousand = 7 ´ 103.
Forming the quotient (7 ´ 1012 ) ¸ (7 ´ 103) = 109, we can say that 7 trillion is 109 or 1 billion times larger than 7 thousand.
22b.
There are several ways to proceed with this estimate. Some people could
estimate the amount a family spends for food more easily than the amount spent
by an individual for food. But let’s assume that a typical individual spends
$30 per week. Then that individual would spend
for
food. This estimate is also subject to considerable error due to the variation
in the amount spent per week.
29. The
conversion factor for the time-line is 100 (102) meters = 15 billion
(1.5 × 1010) years. To convert 1 billion (109) years to
meters, we us the conversion factor:
Similarly,
10,000 (104) years corresponds to
We see
that 1 billion years corresponds to 6.7 meters and 10,000 years corresponds to
about 0.067 millimeters.
37a.
Using a population figure of 280 million people, the daily per capita water use
can be found by dividing by the population:
37b.
Since public water comprises 10% of the total water use, the daily per capita
use of public water is 10% of the daily per capita use of total water (found in
the previous problem) which is 0.10 ´ 1.2 ´ 103 gallons per person per day = 1.2 ´ 102 gallons per person per day. On
average, each person uses 120 gallons of water per day!