How many 400KB files will fit on 1mm^2 surface of hard drive

[Twodogs]

Given that 1.34Tbit of information can fit on a square inch of average hard drive surface, how many 400 KB files could be written on a square millimeter? I did the math and came up with about 634. This seems unbelievably high and I wonder if someone would have time to check it. I kind of need to get it right. My thanks.

 

[mfb]

You have some rounding error, but your result is a good approximation. Hard drives have a huge storage density.

If this is homework, it would fit better to our homework section.

 

[A.T.]

This seems unbelievably high...

What is unbelievable, is that mechanical parts move the head that reads this data, while hovering only few nanometers above it.

 

[Twodogs]

Right, hard to imagine. Any clue as to the numbers?

 

[newjerseyrunner]

Humans have a hard time imagining just how small things get. Once you reach a certain threshold, humans stop seeing adding zeros as increases to the order of magnitude and simply start seeing it as a bigger number.

We're also still several orders of magnitude from our theoretical limit. One bit,takes about a million atoms to store. About a billion atoms need to line up to make a mm, so in a square mm, you have a quadrillion atoms. A few hundred files a few KB each doesn't look like a lot when you think of it that way.

 

[Twodogs]

Thanks, very helpful.
But coming at it with those numbers I get the capacity to store 3.125 400KB files in one mm^2.
That's compared to my first calculation of over 600. Still hard to imagine, but I wonder what number to go with. The smaller is sufficient to make my point.
Any other insights?

 

[Nugatory]

Just an anecdote...
As part of discovery in a legal case, I was once asked to print out three terabytes of ASCII (that's one byte per character!) documents and deliver the hard copy to the lawyers via FedEx overnight service. Eventually the phrase "one hundred fully loaded Boeing 747s" got through to them.

(I knew that I was up against a serious innumeracy problem when they started out by making it quite clear that they wanted everything printed double-spaced, because there was no reason to economize on paper consumption).

 

[russ_watters]

Right, hard to imagine. Any clue as to the numbers?

In post #2 it was said your calc was pretty much correct.

 

[Twodogs]

You have some rounding error, but your result is a good approximation. Hard drives have a huge storage density.

If this is homework, it would fit better to our homework section.

Thanks, but no. The problem is I have been out of school for quite some time.