A Question of Titanic Proportions

The Titanic Iceberg was higher than the deck of the Titanic.
 (Passengers played with the ice after the collision.)
That deck was at least six meters high
(This is a very safe guess, only about twenty feet).

Arctic Icebergs are 6/7 submerged.
( Arctic and Antarctic icebergs have different densities!)

Therefore the iceberg might have been about 42 meters tall top to bottom.
\Let's suppose that the iceberg had an average cross section of a ten meter square.
(Reports say it was a small iceberg, but this would be tiny, a conservative guess)
 The volume of this iceberg would be roughly 4,200 cubic meters of ice (10 X10 X 42)

It would take about 238,095 such icebergs
to make up one cubic kilometer of water.

(1,000,000,000 / 4,200 = 238,095.2381) (I am ignoring the density of ice being .9 that of water,
but I think I still have many orders of magnitude to burn.  A cubic kilometer has
1,000 X 1,000 X 1,000 or a(n American) billion cubic meters in it)

There are 1,444,300,000 cubic kilometers of surface water on Earth (Encyclopedia).

The Titanic Berg tied up about 1 / 343,880,952,400,000
of all the surface water on Earth.
(1 / (238,095 X 1,444,300,000))

Approximately 1 / 3.438806085 X 10^14 of all water molecules on Earth were in the iceberg that ran afoul the Titanic. This number can also be expressed as .000000000000002907983106, or 2.907983106 X 10^-15

Take a breath!

The molecular weight of water is 18 (16[O] + 2 X (1[H])).

There is one mole of water molecules in 18 g of water (This is the definition of a mole), there are 12.8 moles of water in our ice cubes (230 / 18 = 12.7777...)

There are 6.02 X 10^23 molecules in a mole
(This is called Avogadro's Number, and it can also look like this:
602,000,000,000,000,000,000,000),
there are 7.7 X 10^24 molecules in our ice cubes. (12.8 X Avogadro's Number
and it can be written, 7,700,000,000,000,000,000,000,000)

The number of molecules in our ice cubes that represents the proportion of the Titanic's berg to the total water on earth is:
7.7 X 10^24 / 3.438806085 X 10^14 = 2.239149231 X 10^10
or 22,391,492,310.

This assumes that the composition of our ice cubes is representative
of the composition of all the water on the surface of the Earth,
This requires that the iceberg, on melting, and over the last almost 90 years, has distributed itself evenly through all the waters of Earth. This is unlikely, it is more likely to be mostly in the Northern Hemisphere (Less than 1/2 the water on Earth is in the Northern hemisphere). Also, let's suppose that most of the iceberg, as it melted, mixed with the ocean, and has never evaporated, we still have orders of magnitude (Powers of ten) to burn, suppose 1% of 1% of 1% evaporated, we are still left with 2.2 X 10^4 (22,000) molecules in four ice cubes.

That's what I think. What do you think?

With some trepidation and much humility for my efforts and any possible errors or oversights herein, I dedicate this calculation to Cesare Emeliani, once my geology teacher at the University of Miami, who several times performed amazing feats with large and small numbers.  Once he memorably came up with what could possibly pass as the largest meaningful number in the Universe.  Very cool!

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