Answer:
The value of gold in the oceans is 4.07x10¹⁴ $
Explanation:
A problem with relation between the units.
This are the data, 3800 m (depth of the ocean)
The total surface 3.63×10⁸ km² (total surface)
5.8×10⁻⁹g/L (gold concentration)
$1595 (value of each troy oz)
31.1 g (mass of each troy oz in grams)
19.3 g/cm³ (density of gold)
As we have a depth (a kind of height) and the total surface we can know the volume that the ocean occupies. This height is in m, the surface in km².
We should convert eveything in dm to work with concentration.
3800 m to cm = 3800 . 10 = 3800 → 3.8 x10⁴ dm
3.63×10⁸ km² to dm² = 3.63×10⁸ . 1x10⁸ = 3.63×10¹⁶ dm²
(1 km² = 1x10⁸dm)
3.8 x10⁴ dm . 3.63×10¹⁶ dm² = 1.37 x10²¹ dm³
This is the volume that the ocean occupies. By using concentration, we can know the mass of gold in all the ocean.
1L = 1 dm³
1L _____ 5.8×10⁻⁹g
1.37 x10²¹ L ____ 7.9 x10¹² g
So 1 troy oz pays $1595 and 1 troy oz is 31.1 grams, so 31.1 grams pay $1595.
The final rule of three will be
31.1 g __ pay ___ $1595
7.9 x10¹² g ___ pay (8 x10¹¹ g . $1595) / 31.1 g = 4.07x10¹⁴ $
