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### Working with Huge Numbers

```
Date: 05/15/99 at 11:12:55
From: James Sherrington-Kendall
Subject: Is there anywhere on the Internet I can work out EXTREMELY
big numbers?

Dear Sir,

I am trying to find either a good program or a Web site where I can
work out rather large numbers. If not, I would be grateful if you
could tell me a method for working out a number such as 4 to the
power 300 billion.

Thanks ever so much,
Chez
```

```
Date: 05/17/99 at 13:37:39
From: Doctor Peterson
Subject: Re: Is there anywhere on the Internet I can work out
EXTREMELY big numbers?

Hi.

What you need depends on what you need it for. If you want a program
to calculate large numbers precisely, there are arbitrary precision
calculators that will give hundreds of digits, such as this:

http://www.geocities.com/SiliconValley/2548/BigCalculator.html

Unfortunately, it seems to make my computer slow down horribly, so I
don't recommend it. You might find more by searching the Web for
"arbitrary precision."

However, you may not need all that precision (that is, all the digits
of your answer), and if you don't you should use a different method,
because working with many digits puts a big load on your computer. In
your example, 4^300,000,000,000 would take 180,617,997,399 digits just
to write out, or something like 37,000,000 pages. You won't find a
calculator that can handle this exactly.

How did I figure that out? Many large calculations can be done easily
(but only approximately) using logarithms. We can first find the
logarithm of your number this way:

log(4^300,000,000,000) = log(4) * 300,000,000,000
= 0.602059991328 * 300,000,000,000
= 180617997398.4

then undo the log by raising 10 to this power. The calculator will
complain if you do this last step directly, because it can't handle
such large numbers; but we can break it down:

4^300,000,000,000 = 10^180617997398.4
= 10^180617997398 * 10^0.4
= 2.45 * 10^180,617,997,398

That's the 180,617,997,399-digit number I mentioned!

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculators, Computers

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