Physics for Scientists & Engineers & Modern Physics, 9th Ed

 42. Review. The average density of the planet Uranus is 
1.27 3 10
3
kg/m
3
. The ratio of the mass of Neptune to 
W
W

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18
chapter 
1
physics and Measurement
If the sidewalk is to measure (1.00 6 0.01) m wide by
(9.0 6 0.1) cm thick, what volume of concrete is needed 
and what is the approximate uncertainty of this volume?
Additional Problems
 54. Collectible coins are sometimes plated with gold to 
enhance their beauty and value. Consider a commemo-
rative quarter-dollar advertised for sale at $4.98. It has 
a diameter of 24.1 mm and a thickness of 1.78 mm, 
and it is completely covered with a layer of pure gold
0.180 mm thick. The volume of the plating is equal 
to the thickness of the layer multiplied by the area to 
which it is applied. The patterns on the faces of the 
coin and the grooves on its edge have a negligible effect 
on its area. Assume the price of gold is $25.0 per gram. 
(a) Find the cost of the gold added to the coin. (b) Does 
the cost of the gold significantly enhance the value of 
the coin? Explain your answer.
 55. In a situation in which data are known to three signifi-
cant digits, we write 6.379 m 5 6.38 m and 6.374 m 5 
6.37 m. When a number ends in 5, we arbitrarily choose 
to write 6.375 m 5 6.38 m. We could equally well write 
6.375 m 5 6.37 m, “rounding down” instead of “round-
ing up,” because we would change the number 6.375 by 
equal increments in both cases. Now consider an order-
of-magnitude estimate, in which factors of change 
rather than increments are important. We write 500 m 
, 10
3
m because 500 differs from 100 by a factor of 5 
while it differs from 1 000 by only a factor of 2. We write 
437 m 
, 10
3
m and 305 m 
, 10
2
m. What distance dif-
fers from 100 m and from 1 000 m by equal factors so 
that we could equally well choose to represent its order 
of magnitude as 
, 10
2 
m or as 
, 10
3
m?
 56. (a) What is the order of magnitude of the number of 
microorganisms in the human intestinal tract? A typi-
cal bacterial length scale is 10
2
6
m. Estimate the intes-
tinal volume and assume 1% of it is occupied by bacte-
ria. (b) Does the number of bacteria suggest whether 
the bacteria are beneficial, dangerous, or neutral for 
the human body? What functions could they serve?
 57. The diameter of our disk-shaped galaxy, the Milky Way, 
is about 1.0 3 10
5
light-years (ly). The distance to the 
Andromeda galaxy (Fig. P1.57), which is the spiral gal-
axy nearest to the Milky Way, is about 2.0 million ly. If a 
scale model represents the Milky Way and Andromeda