How long for a computer to write out a Googolplex

[MathJakob]

Just curious, for a start, I don't think there is enough hard drive space in the world to document the number but if a computer could printout 100 billion 0's a second, how many years would it take before the computer had printed out the full number?

I have no idea how to possibly work this out, I tried using Wolfram but I don't even know how to type lol.

A googolplex is an extremely large number, often used informally to refer to a number that is far greater than anything that has practical relevance. It is defined as 10 to the power of a googol, where a googol is 10 to the power of 100. In other words:

1 googol = 10^1001 googolplex = 10^(10^100)

 

[Mark44]

Just curious, for a start I don't think there is enough hard drive space in the world to document the number but if a computer could printout 100billion 0's a second, how many years would it take before the computer had printed out the full number?

I have no idea how to possibly work this out, I tried using wolfram but I don't even know to type lol.

A Googol is 10¹⁰⁰, which is 1 followed by 100 zeroes.
How big is a Googolplex?

 

[SteamKing]

All your answers are here:

http://en.wikipedia.org/wiki/Googolplex

 

[MathJakob]

A Googol is 10¹⁰⁰, which is 1 followed by 100 zeroes.
How big is a Googolplex?

Googolplex is $$10^{googol}$$

Also no SteamKing that does not answer my question unfortunately. It mentions nothing about a computer being able to printout or run through 100billion 0's per second.

I know there is not enough room to write the number out, but if there was, how long would it take a computer printing 100billion 0's per second?

 

[Mark44]

Googolplex is $$10^{googol}$$

So what is this number without the word "googol"?

Also no SteamKing that does not answer my question unfortunately. It mentions nothing about a computer being able to printout or run through 100billion 0's per second.

I know there is not enough room to write the number out, but if there was, how long would it take a computer printing 100billion 0's per second?

100 billion is 1 X 10¹¹ (by American reckoning, with 1 billion being 1,000 million).

This problem isn't hard if you write the numbers in scientific notation.

 

[SteamKing]

The googolplex = 10^(10^100)

If there isn't enough material (and enough atoms) in the universe with which to print the value, its pretty safe to say that the time required > the age of the universe.

 

[MathJakob]

You're not listening to what I'm saying... I'm not talking about printing the number out onto physical objects, I said this many many times. I simply want to know, if a computer can read 100 billion 0's per second, then how many years will that computer take, until it's read through the entire number.

How hard is it to get an answer around here... I'm terrible at maths cmon guys.

 

[phyzguy]

It's not that hard. A googolplex is 10^(10^100). If you print out 10^11 zeros per second, then it will take

t = 10^(10^100) / 10^11 = 10^(10^100-11) = 10^(10^100) seconds
t = 10^(10^100) / (3*10^18) = 10^(10^100-18.5) = 10^(10^100) years

Where the last equality in each line is approximate, since I'm ignoring 11 (or 18.5) compared to a googolplex. However, this is a very, very good approximation.

So the answer is that it will take a googolplex seconds or a googolplex years, both of which are about the same, and both of which are an incomprehensibly long time.

,

 

[jbriggs444]

It's not that hard. A googolplex is 10^(10^100). If you print out 10^11 zeros per second, then it will take

t = 10^(10^100) / 10^11 = 10^(10^100-11) = 10^(10^100) seconds
t = 10^(10^100) / (3*10^18) = 10^(10^100-18.5) = 10^(10^100) years

That's how long it would take to count to a googolplex. The challenge at hand is how long it would take to print a googolplex.

That does not take 10¹⁰¹⁰⁰ operations. It only takes 10¹⁰⁰ operations. SteamKing has already referenced a page that provides a time estimate. The only difference is that his reference used an assumption of two zeroes per second rather than 100 billion.

 

[phyzguy]

My mistake. So let me re-do my estimate:

t = 10^(100) / 10^11 = 10^(100-11) = 10^89 seconds
t = 10^(100) / (3*10^18) = 10^(100-18.5) = 3*10^81 years

Still an extremely long time, but not so incomprehensible.

 

[Brian121268]

so that's 30 sexvigintillion years, (3,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years) or 1/10 novemvigintillion seconds, (100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 seconds) if the math is correct. according to http://bmanolov.free.fr/numbers_names.php

I guess. my brain shuts down after 6 zero

I assume that is how long it takes for the computer to do it. If so, my best guess as to how long it would take to count out is: Go get in your car right now. Start driving, any direction, at about 75 mph. Now drive to the very edge of the universe. Return home. You might have done it by now. If not, you may need to repeat.