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| Math Central | Quandaries & Queries |
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Question from Pete, a student: how would you find the number of digits in a really big exponent without a calculator? |
Pete,
Do you want just a rough estimate or a very accurate one? First, if you have a number like 3.65 x 1069 you should see that there are 70 digits - it's the power of 10 that is important (why is it 70 and not 69?).
Suppose you have 284. Since 210 = 1024 ~ 1000 = 103 then 284 = 16 x 280 ~16 x (103)8 and that's 'about 16 x 1024 and it has about 26 digits.
If you have 2748 however life is not so easy. You would need to use logarithms to handle your question in this case. If this is what you need, write back,
Penny
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