Displaying Large Repetends on Small Calculators
Date: 05/31/2002 at 13:02:45 From: Jack Carter Subject: repeating decimal form of rational number The approximation 1/7 = .142857142857142857 where the '142857' is the 6-digit repetend, is easy to display on a calculator, but 1/17 has a 16-digit repetend. How can I display this repetend on a calculator? Is there a general procedure for the ratio of two integers a/b?
Date: 05/31/2002 at 16:43:09 From: Doctor Peterson Subject: Re: repeating decimal form of rational number Hi, Jack. Obviously you can't display all 16 or more digits on an 8-digit display; but you can get, say, 6 or 8 digits at a time with a little effort. Imagine dividing by hand; at each step you would have a remainder (less than 17) and if you stop at some point, you can continue on to the next digits knowing only that remainder. So all you have to do is find the remainder after however many digits you can see, and then continue from there. For example, if you have the digits 1/17 = 0.0588235 which is the same as saying that 10000000/17 = 0588235, the remainder at this point is 10000000 - 0588235*17 = 10000000 - 9999995 = 5 so you can find the next set of digits by dividing 5000000/17 = 294117 This gives us the digits 0.0588235 294117 You can repeat, using the remainder from the last division: 5000000 - 294117*17 = 5000000 - 4999989 = 11 11000000/17 = 647058 so we are now up to 0.0588235 294117 647058 and we've started repeating. (To verify that it is actually repeating, you can find the remainder at the start and end of the suspected repetend, and check that they are the same.) Here are some related answers from our archives: http://mathforum.org/library/drmath/view/58169.html http://mathforum.org/library/drmath/view/54339.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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