The data in this exam are a set of 6 integers a through f, based on your social security number. Write the LAST 6 digits of your social security or ID number in the spaces below, to define a through d:
 
___      ___      ___      ___      ___      ___      ___      ___   ____
                                      ||            ||           ||          ||          ||         ||
                                      a          b            c         d          e        f
 
Because of the mechanics of the calculations, it is necessary that a is less than b, that c is greater than d, and that all of [a b c d e f] are greater than zero. So, make changes in your digits if necessary. If two students use the same [a b c d e f], they will be asked to rework the entire exam (so save your calculations in the unlikely event that this happens). The data [2 3 7 6 4 6] cannot be used, because they appear in the sample at the end of this document. Work all problems using the same set of [a b c d e f].  For the purposes of turning in your test, define "m1" to be the "a" that you use, "m2" to be b, "m3" to be c, "m4" to be d, "m5" to be e, and "m6" to be f.

1. If you require a certain number of significant digits in a final answer, you must maintain more digits in the intermediate calculations. For instance consider the addition 1/3 + 1/3 = 2/3. The three-significant-digit expression for the answer, 2/3, is .667 . But if you first round the addends to three significant digits you get .333 + .333 = .666, which is not correct to 3 digits. A good rule of thumb is to retain at least two more digits than required, in all intermediate calculations.

2. Always introduce symbols (letters) when you evaluate a formula, especially on a calculator. For instance suppose you wanted to add 436 and 578 on a calculator. The worst way to do it is to enter 436, press enter, press +, enter 578, press enter, and press =. Because: suppose you get an answer that you know is wrong, like -23. You don't know whether you entered the 436 wrong, or the 578, or the + sign. You have to reenter all the data again. The smart way is to let A equal 436, let B equal 578, and call for A+B. If the answer is absurd, you can recall A, B, and the formula; and you can correct only the one that's wrong. This is particularly significant when you're dealing with high-digit numbers, and complicated formulas that may require parentheses.