Repeating Decimals and FractionsDate: 11/27/2001 at 20:59:25 From: Lisa Paez Subject: Changing repeating decimals into fractions I have a chart of repeating decimals and their fraction equivalents. The decimal is .71 and they give a fraction of 5/7. I cannot figure out how (step by step) they came up with this number. I came up with 71/100 and not think it would reduce any further than that. Another is .4545; the chart says that should be 5/11, and I can't explain that either. Thank you, Lisa Paez Date: 11/28/2001 at 00:15:56 From: Doctor Tom Subject: Re: Changing repeating decimals into fractions Hi Lisa, The chart is wrong. Here's how to do it, by means of examples: .71717171... (continuing the alternating 71 forever) = 71/99 .123123123... = 123/999 .71428571428571428575... = 714285/999999 = 5/7 Trickier are these types: .1112323232323... (just the 23 repeats) = 111/1000 + (1/1000)(23/99) The easy way to see this is that: .11123232323... = .111 + .00023232323... = 111/1000 + (1/1000)(.232323...) All others can be handled similarly. Just for fun, why don't you try the reverse for the fraction 1/81? Find the decimal expansion that repeats. - Doctor Tom, The Math Forum http://mathforum.org/dr.math/ |
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