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/
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