Power of 120Date: 06/12/2001 at 11:43:09 From: Grabowski Subject: Exponents Is there a quick way to work out 1.05 to the power of 120? The only way I can think of is to take 1.05 and keep multiplying it by itself, 120 times. Date: 06/12/2001 at 12:31:37 From: Doctor Peterson Subject: Re: Exponents Hi, Grabowski - I would use a scientific calculator, which has an exponent key. (My computer has one in the Accessories menu.) If I had to do it by hand, I would save some work by repeatedly squaring, rather than just multiplying by 1.05 itself. You can then multiply some of these powers together to get what you want. As an example, 1.05^5 is 1.05^4 * 1.05^1, so you can calculate it by squaring until you get 1.05^4 1.05^1 = 1.05 1.05^2 = 1.1025 1.05^4 = 1.2155 and then multiplying 1.2155*1.05=1.276. This took only three multiplications rather than 4; for larger exponents the savings will be much greater. In your case, I would square 6 times until I got 1.05^64, and then multiply four of these numbers together, so it takes only 9 multiplications. If you've learned about the binary number system at all, you'll find that to be helpful. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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