Math 2000 - Solutions 4

Fall 2000

6b. Because 1 million is 10⁶, 7 million is 7 ´ 10⁶

6c. Because 1 billion is 10⁹, 1 billionth is 10^-9, and 9 billionths is 9 ´ 10^-9.

8b. 0.92 = 9.2 ´ 10^-1.

8c. 500.098 = 5.00098 ´ 10².

12b. The area of the Earth’s surface is 5.096 ´ 10⁸ square kilometers.

14c. (9 ´ 10³) ´ (5 ´ 10^-7) = (9 ´ 5) ´ (10³ ´ 10^-7) = 45 ´ 10^-4 = 4.5 ´ 10^-3

14d. (4.4 ´ 1099) ¸ (2.0 ´ 1011) = (4.4 ¸ 2.0) ´ (10⁹⁹ ¸ 10¹¹) = 2.2 ´ 10^{99 - 11} = 2.2 ´ 10⁸⁸

18d. Note that 7 trillion = 7 ´ 1012 and 7 thousand = 7 ´ 103. Forming the quotient

,

we can say that 7 trillion is 109 or 1 billion times larger than 7 thousand.

23b. Let’s assume that the walk across the United States is 3200 miles long, that the walker can cover 2 miles per hour and can walk 8 hours per day. The walker can cover 16 miles per day. Thus the entire trip takes (use units!)

We see that the walk can be done in a year (365 days) even if some of the assumptions are relaxed.

29. The conversion factor is 100 m = 15 billion years. Therefore 1 billion years is

Similarly 10, 000 years = 10⁴ years is

Human history is 0.067 mm from the present on the timeline.

37a. Using a population figure of 260 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 ´ 1.3 ´ 10³ gallons per person per day = 1.3 ´ 10² gallons per person per day. On average, each person uses 130 gallons of water per day!