Converting a Mixed Decimal to a Fraction
Date: 11/09/2001 at 13:54:23 From: Kathryn Leist Subject: Converting mixed decimal to fractions I am homeschooling an 8th grader. We have not been able to locate how to do this problem: Write 4.16 2/3 as a mixed number. We know the answer is 4 1/6. We just can't figure out how they reached that. When I was in school we just did repeating decimals and not fractions. Is this a new learning style? Thank you!
Date: 11/09/2001 at 17:01:44 From: Doctor Peterson Subject: Re: Converting mixed decimal to fractions Hi, Kathryn. You can read about this notation in our archives: Clarifying Fraction Notation http://mathforum.org/dr.math/problems/goetzke7.2.97.html I wouldn't call it new, just rare. As Dr. Sonya said in that answer, this is not considered a standard notation; but it is sometimes seen, perhaps in certain fields that we are not familiar with as mathematicians and scientists. I think it would probably arise most often in converting from a percentage; 83 1/3% could naturally be written as 0.83 1/3, meaning (83 1/3)/100. This is confusing, and I wouldn't teach it as something to do deliberately, only as something one should be able to understand when we come across it. Like certain obsolete or vulgar words, it may be worth having as part of your "reading vocabulary," but should not be in your normal "speaking vocabulary." In reading this notation, you have to think of the fraction as part of the last digit, not taking a decimal place of its own. In your example, 4.16 2/3 would mean 4 + 1 tenth + 6 2/3 hundredths, or 4 + 16 2/3 hundredths, not as 4 + 1 tenth + 6 hundredths + 2/3 thousandth. The ambiguity as to where the fraction belongs is the reason we recommend not using this notation. But again, in a context where you expect two decimal places, and want to be more precise (as in percents, or in money situations like 83 1/3 cents), there may be some value in mixing fractions with decimals. To work out your problem, multiply the number by 100 to get rid of the decimal point, and then divide by 100 as a fraction to get back to the intended value: 416 2/3 1250/3 1250 125 25 4.16 2/3 = ------- = ------ = ---- = --- = -- = 4 1/6 100 100 300 30 6 You can save some work by taking the 4 off and putting it back on at the end: 16 2/3 50/3 50 1 4 + .16 2/3 = 4 + ------ = 4 + ---- = 4 + --- = 4 + --- = 4 1/6 100 100 300 6 I'm curious as to which book teaches this; since we do get questions on this from time to time, clearly someone teaches it, but probably not many texts do so. It seems particularly odd, though, that the text itself wouldn't explain it; it must have been taught earlier in the series. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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