Rounding Negative and-a-Half Up or Down
Date: 11/10/2010 at 05:37:31 From: Geoff Subject: rounding negative decimal numbers To whom it may concern, We are grade 7 students from Riffa Views International School in Bahrain. We are currently studying a unit on fractions, decimals and rounding in math -- and we have a small dilemma. We are trying to figure out if you have a negative decimal like -3.5, should you round it to -4 or -3. We have already learned that for positive numbers, five tenths or more should be rounded up, while four or less should be rounded down. We think that 5 goes with 6, but we have searched the Internet and found a number of different answers for -3.5. Some say you should round up and some say you round down. Also, we wonder if negative being opposite means that the rules for a negative number should be opposite as well. If so, -3.5 should be rounded to -4. But if .5 should be rounded up, then it would be -3 because -3 is more than -4. We appreciate your answers and look forward for your reply. Best Regards, Grade 7 students at RVIS Riffa Views International School Bahrain http://www.rvis.edu.bh/
Date: 11/10/2010 at 13:07:12 From: Doctor Peterson Subject: Re: rounding negative decimal numbers Hi, Geoff and class. That's a good question, and you've done some great thinking. The quick answer is that it doesn't matter much, if at all. Here's why: Think first about the meaning of "rounding to the nearest integer," which is the full name of what you are doing. You are looking for the closest integer to the given number. For example, you round 3.42 to 3 because it is closer to 3 than to 4. You round -4.78 to -5 because it is closer to 5 than to 4. Now, what about 3.5? It's the same distance from 3 and 4, so there really IS no nearest integer. Either 3 or 4 would be equally good as an answer. The same is true of -3.5: it's exactly between -3 and -4. Whatever answer you give, it is an arbitrary choice -- and there are several ways to make that choice. It's common to choose to round 3.5 up to 4 (which appears to be the rule you have been taught) simply because it's the easiest rule to learn and use. Any other number with a 5 in the tenths place, such as 3.51, will round up because it is closer to 4 than to 3; so we lump 3.5 together with all those and say we'll round up whenever the tenths place is 5 or more. Following that rule (keeping the goal of simplicity), we would round -3.5 to -4 because -3.51 rounds to -4. So the rule is to round "away from zero" when the tenths digit is 5 or more. But there are other choices. Here are some pages on which we have talked about this (aimed at people at various levels, so some will be of more interest to your teacher or parents than to you): Rounding Decimals: Even/Odd Issues http://mathforum.org/library/drmath/view/58972.html Are There Times When Following the Rounding Rules Isn't Best? http://mathforum.org/library/drmath/view/70605.html Rounding Negative Numbers http://mathforum.org/library/drmath/view/71202.html Teaching Rounding Rules http://mathforum.org/library/drmath/view/63989.html Ultimately, there is no one standard way to round negative numbers that are exactly halfway; you can choose your preferred rule and use that. Probably you'll find that the one I suggested is easiest. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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