Order of Operations with PercentagesDate: 04/05/2001 at 15:27:44 From: james Subject: Order of operations and percentage Why does the order of operations exclude percentage, square roots, etc.? Let's say I have a problem like this: 5% of 290 + 89 square root - 1 = Date: 04/05/2001 at 23:11:17 From: Doctor Peterson Subject: Re: Order of operations and percentage Hi, James. I think we avoid listing all these special things so we don't overwhelm students. Computer programming languages have to spell out exactly what every possible combination of symbols means, so they give big lists of rules, and it can be pretty scary to learn. In real life, we usually just try to avoid writing anything that looks too tricky, because people don't follow rules as well as computers. The percent sign and square root sign are "unary operators"; that is, they act on one number to the right or left. They are probably always at the top of the list, the first things you have to evaluate. For example, 3+5% would mean 3 + 0.05 = 3.05, not 8% = 0.08. The square root sign is special. The actual radical sign is just the "v"-like thing alone, and means to take the root of the number following it. For example, \/4+5 would be 2+5=7, not the square root of 9, which is 3. But you usually see a bar hanging over the numbers you are to operate on. That part of the symbol is called a vinculum, and is left over from a time when that was used instead of parentheses. So ____ \/4+5 does mean the square root of 9. I answered a similar question about a more complicated operation, the factorial, which you may not have heard of; but the ideas I expressed there are useful here as well: Factorials and Order of Operations http://mathforum.org/dr.math/problems/kiaran.09.21.00.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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