Sci. Notation and Order of Operations

[ag88man]

I have a question about order of operations.

On the TMSCA calculator contest within a problem 9 X 10^-4 is seen as a single number.

So if 9/9 X 10^-4 is calculated the result of 10,000 is given on the answer key.

But if you don't recognize 9 X 10^-4 as a single number the result of the same problem is 0.0001
(Try 9/9 X 10^-4 without using the EE key with a non RPN calculator or just do it by hand)

Is recognizing scientific notation as a single number a rule of the contest or is this a general order of operations rule?

I could not get an answer other than "that is the way it has always been done" from the judge at the last TMSCA contest, and
I was hoping for a more complete answer.

On a related note:
I understand that 1 over 2 = .5 ,but I always thought that was because the vinculum is a recognized grouping symbol, not because it was in fraction notation.

Thank you in advance.

[sexyasiangirl]

By 9/9 X 10^-4, I'm guessing you mean 9/.0009. This would be the same as 9/(9 x 10^-4), but NOT (9/9) X 10^-4, because you are dividing by the expression (9 x 10^-4), so the entire thing flips when you divide. For example, if you're dividing 36 by 6, this would be the same as 36/(3*2), but not (36/3)*2.

[ag88man]

My problem is the "having to guess."

The problems do not have parenthesis around the 9 X 10^-4

Examples of problems that will give multiple answers because of this situation are #19, #23, #27, and #42 on the TMSCA Calculator Contest #13 given on February 21, 2009.

[AuSmith]

Yes, there is some guessing. It's unfortunate. Problems are supposed to be stated clearly so that the difficulty lies in the solution. Duh. I thought one of Bourrell's problems at 2005 UIL State was ambiguous, so I asked him what I did wrong. He started to interpret his problem the same way I did, then remembered the "correct" interpretation saying, "That trips me up, too." Seemed to me, if he's confusing himself, he has little hope of communicating the problem clearly to a significant percentage of contestants. Moreover, if he knew his problem confused his own natural interpretation, why wouldn't he try to make it clearer? Calc apps is laden with ambiguity. Take the AMC 10/12 instead! Haha.

You might argue that writing [unparseable or potentially dangerous latex formula] isn't as interesting, so you should assume that the [unparseable or potentially dangerous latex formula] is done first.

[B3ndythumbs]

okay sorry to intrude but i have a question on sig figs. usually on the stated parts, there is a SD problem. how do u determine how many sig figs are in the answer?

[jahu]

follow the rule of sig figs in the problem

[B3ndythumbs]

uhh...which is?

[jahu]

For multiplication and division, the result should have as many significant figures as the measured number with the smallest number of significant figures.

For addition and subtraction, the result should have as many decimal places as the measured number with the smallest number of decimal places.

from wikipedia

[AuSmith]

The accuracy of multiplication depends on how many significant digits you have (insignificant digits would be place holding 0's, which don't provide any more accuracy, but only order of magnitude), and accuracy in addition depends on where the last significant digit is. The best illustration is some figure like [unparseable or potentially dangerous latex formula]. If you were to add it to something, it shouldn't affect the result very much. So, it would be used with high precision. If you multiply by [unparseable or potentially dangerous latex formula], it greatly affects the number. And, with the large margin of error from keeping only two sig figs, it would be used with low precision.

Exact numbers have an "infinite" number of sig figs. Think of the endless 0's after the decimal as significant, because they attest to the true value of the number. You only need to worry about measured values which are the underlined figures.

Special case: if a figure ends in a decimal, or the last 0 comes after the decimal, all the digits are significant. E.g. [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. both have five sig figs. Also, an overline over a [unparseable or potentially dangerous latex formula] means that is the last significant digit.

Ex: [unparseable or potentially dangerous latex formula]

First, we kept only two significant digits because [unparseable or potentially dangerous latex formula] was the "limiting reagent," then we rounded to the nearest ten-thousandth's place because [unparseable or potentially dangerous latex formula] was the limiting reagent.