Final answer:
The greatest ocean depth compared to Earth's diameter is approximately 0.000821 and the greatest mountain height is approximately 0.000694. Rounded to the closest options provided, both fractions are closest to 0.0001, which corresponds to option 'b'.
Step-by-step explanation:
To answer question 34 (a) and (b), we need to compare the greatest ocean depth and the greatest mountain height to Earth's diameter. Let's first convert the greatest ocean depth, approximately 6.5 miles, to kilometers, knowing that 1 mile equals approximately 1.60934 kilometers. So the greatest ocean depth in kilometers would be 6.5 miles * 1.60934 km/mile ≈ 10.461 km. Next, we use the average diameter of Earth, which is roughly 12,742 km. The fraction for the greatest ocean depth compared to Earth's diameter is then 10.461 km / 12,742 km ≈ 0.000821.
Now, regarding the greatest mountain height, the height of Mount Everest is approximately 8.848 km. Using the same Earth's diameter, the fraction is 8.848 km / 12,742 km ≈ 0.000694. Neither of these exact numbers appear in the options provided; however, if we round to the nearest order of magnitude to match the options, we find that the ocean depth fraction is closer to 0.001 and the mountain height fraction is closer to 0.0001. Thus, the best approximations from the options provided would be: (a) 0.0001, (b) 0.0001, which corresponds to choice 'b'.
Note
: In certain contexts, the precision of the answer could be crucial, and the rounding method employed here was based on the available options. The fractions obtained in this exercise should be treated as approximations for comparative purposes. In a scientific setting, more exact figures would likely be required.