(Adapted from a "diatribe" by Prof. Allen)
Suppose you have to enter the number 1.66 x 10-27. No problem. You do 1.66 EE chg sign 27. EE means the "enter exponent" button. You can change the sign before or after entering the 27, at least on my calculator. But now suppose you want to enter the number 10-14. You do 10 EE chg sign 14, right? Wrong! Try it. your calculator will give 1.000... E-13 which means 10-13! If you think about it, it makes sense. The sequence 10 EE chg sign 14 means 10 x 10-14 which is 10-13. The best thing to do is to remember to enter 1 EE chg sign 14. I thought you might like to know this! Probably you did already. I used to have a calculator which allowed you to do just EE chg sign 14. It was smart enough to know that there was a 1 there. I miss my old calculator.
Computers (I'm sure you found this out!) are amazingly dumb, and don't always support raizing numbers to a power. For instance,
"What is the decimal equivalent of 2.8 x e-4 ?"
If you answered:
"The correct answer is 0.00028"
I am sorry, but I have to disagree! All physicists would agree that the correct answer is actually 5.1 x 10-2. We would of course also recognize 0.051 as a correct answer (the "decimal equivalent"). The symbol e is a number, 2.7183..., and not 10. When computers were first programmed in languages like Fortran, an alternate version of scientific notation was needed, and the number 2.8 x 10-4 became 2.8E-04, since punch cards had no way of doing a superscript. But E is not e. Pocket calculators can rectify this ugly (but successful) notation, because their displays can easily be designed to write superscripts. Some calculators write 2.8-04 as a shorthand and it's unfortunate that they didn't throw in the missing "x10". The next step is that results are transcribed back to good old paper using pencil. What gets written? All sorts of stuff. Here are 6 sensible (?) possibilities. Of these, only the first is pleasing to me, and the second is marginally correct. The rest are wrong.
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2.8x10-4 |
Excellent |
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2.8E-04 |
Ugly! Not OK unless you're writing on a computer. This notation was good for circa 1964 computers, but not OK for 21st century physics. You may loose credit for this on an exam. |
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2.8e-04 |
Worse! Dangerous because e also means ~2.7183. This will be counted as incorrect on an exam! |
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2.8E-04 |
Wrong! What is E raised to the power -4 supposed to mean? You will loose credit. |
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2.8-04 |
Wrong. This means 2.8 raised to the power -4. When my pocket calculator does it, I know that it always means scientific notation, but as a written number, it is at best highly confusing. You will loos credit |
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2.8e-04 |
Wrong! This means something else! How can we allow ex to mean 2.7183... raised to the power x some of the time, and 10 raised to the power x some of the time? You will loose credit |