My 7 year old son asked me a cool question. Using the number
ducentillion (10^603)grains of beach sand, how big of an area of space
in volume would this consume in our own milkyway? Ofcourse I'm
specuating and assuming the heat and gravity of such a mass would melt
the sand into a giant ball of liquid glass. The outer portion would be
solid glass, while the inside core would be molton.  I believe my son
want's to know the relivencey of this huge number. So far, we can't
seem to grasp a comparison to anything. Moreover, I don't believe
there is even ducentillion particles of dust in the univerce. What do
you think--gueniuses? P.S. How many of our own suns could we fill with
such a number?

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Clarification of Question by ducentillion-ga on 01 Feb 2006 16:52 PST

since ducentillion particles of beach sand is to large of a sand box,
maybe my son would understand the size of this number if we use Quarks
as the particle.
So now, can't we use how many Quark particles would be in the mass of
one grain of beach sand? This way there should a much closer number to
10^603 in size to represent an area concievable to imagine for a 7
year old curious mind.
Thank you.

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Clarification of Question by ducentillion-ga on 02 Feb 2006 05:38 PST

Ok--you win. As Jesus said "It is finished!". So why did someone
create a name and value for such a number in the list of large
numbers?

http://www.answerbag.com/q_view.php/16843

"Now, if you were wondering how many grains of sand it would take to
fill the observable universe, this question could be answered.
According to the World Book Encyclopedia, "Scientists define sand as
grains that measure from 1/400 inch (0.06 millimeter) to 1/12 inch
(2.1 millimeters) in diameter.", so if we take a medium sized grain
with a diameter d = 1.02 mm then the volume of the sand Vs =
(4/3)*Pi*(d/2)^3 = .556 mm^3. From Wikipedia, the comoving volume of
the observable universe (assuming that the region is perfectly
spherical) is 1.9x10^33 ly^3. So now we need to either convert ly^3 to
mm^3 or vice versa, so I guess we'll convert the size of the
observable universe to mm^3. Big numbers are always fun. 1 ly =
9,460,730,472,580,800 m ~ 9.46x10^18 mm => 1.9x10^33 ly^3 = 1.61x10^90
mm^3. So, (1.61x10^90 mm^3)/(.556 mm^3) = 2.89x10^90 grains of sand."

Have a good day.

Now, if only your son had lived a couple thousands years ago, he might
now be famous. This is exactly the problem Archimedes attacked in his
essay "The Sand Reckoner". He was hampered by a horrible method of
expressing numbers and had to invent an early form of scientific
notation in which he talked about powers of a myriad myriad (10^8). He
underestimated the size of the universe and came up with 8*10^63
grains of sand to fill the universe. The correct answer (as above) is
vastly larger than this, but incomprehensibly smaller than a
ducentillion.

10^603 is just way too big. Using quarks is problematic. As far as we
know, they are point particles with no size whatsoever, just like
electrons. On the other hand, they never travel alone and cannot be
isolated. Let's use the size of one of the smallest collections of
quarks, the proton or neutron, which has a diameter of about 10^-15 m.
The universe has a diameter of about 2*10^10 light years, a light year
is about 10^16 m, so the diameter of the universe is about 2*10^41
times the diameter of a proton. Cube that and you get about 10^124,
still an incomprehensible factor of 10^479 away from the ducentillion.

Let's try one more step. According to string theory, there are no
point particles. The size of the smallest particles is about equal to
the Planck length, 10^-35 m or 10^20 times smaller than the proton.
This gives us another 60 orders of magnitude more particles when we
fill the universe, but that still only takes us to 10^184, still
inconceivably smaller than 10^603.

"So why did someone create a name and value for such a number in the
list of large numbers?"

Because they could.

It's really meaningless. I mean, look at the previous discussion - all
scientific notation and no terms like "ducentillion".