16. The sun, on average, is 93 million miles from the Earth. How many meters is this? Express (a) using power of ten, and (b) using a metric prefix.
a) 93 * 10^6 mi = 93 * 10^6 * 1.61 * 10^3 m = 149.73 * 10^9 m
b) 149.73 * 10^9 m = 149.73 * gegam
17. A typical atom has a diameter of about 1.0 * 10^-10 m. (a) What is it in inches? (b) How many atoms are there along a 1.0 cm line?
a) 1.0 * 10^-10 m = 1.0 * 10^-10 * 39.37 in = 39.37 * 10^-10 in
Good. That would then be expressed as 3.937 * 10^-9 in.
b) 10^8 atoms
18. Express the following sum with the correct number of significant figures:
1.00 m + 142.5 cm + 1.24 * 10^5 μm =
1.00 m + 142.5 * 10^-3 m + 1.24 * 10^-1 m =
1.00 m + 0.1425 m +0.124 m =
1.2665 m
1.00 m is significant only to the second decimal place, so your answer is also limited to this precision. You would need to express the result as
1.27 m.
19. Determine the conversion factor between (a) km/h and mi/h, (b) m/s and ft/s, and (c) km/h and m/s.
a) 1 km/h = 0.621 mi/h
b) 1 m/s = 3.28 ft/s
c) 1 km/h = 0.278 m/s
20. How much longer (percentage) is a one – mile race than a 1500 – m race (in metric mile)
1 mi = 1.61 *10^3 m > 1500 m
On 110 m 1 mi > 1500 m
110 m = 6.83% of 1 mi
21. A light- year is the distance light (speed = 2.998 * 10^8 m/s) travels in 1.00 year.
How many meters are there in 1.00 light- year?
1 year = 3.156 * 10^7 s
speed = 2.998 * 10^8 m/s
distance = speed * time = 2.998 * 10^8 m/s * 3.156 * 10^7 s = 9.461688 * 10^15 m
22. The diameter of the moon is 3480 km. What is the surface area, and how does it compare to the land surface area on the Earth?
Radius of the moon = 3480 / 2 km
Radius of the Earth = 6.38 * 10^3 km
Surface area of the moon = 4 * π * R^2 = 4 * 1740^2 * π =12110400 π km
Surface area of the Earth = 4 * (6.38 * 10^3) ^2 * π =162817600 π km
The surface of the Earth in 13.444 times larger than the surface of the moon.
When you square the radius you get units of km^2; your areas would therefore be expressed in km^2.
23. Estimate the order of magnitude (power of ten) of:
a) 7800 ≈ 10^4
b) 9.630 * 10^2 ≈ 10^3
c) 0.00076 ≈ 10^-3
d) 150 * 10^8 ≈ 10^10
24. Estimate how long it would take a good runner to run across the United States from New York to California.
Distance ≈ 2501.0 miles = 4024.0 km
Speed (Ben Johnson, Canada) ≈ 36.77 km/h
Time ≈ 4024.0 km / 36.77 km/h ≈ 109.437 h = 4.56 days
Good estimate, except that Ben Johnson was a sprinter-middle distance runner. He could move that fast for only about a minute. He would also have to eat, sleep and rest. An actual runner would in fact require more than a month.
This looks very good. See my notes and let me know if you have questions.