I was doing in long division dividing 9 by 8 and that by 7 and that by 6 and so forth the other day and I got the result of .0002232142857 (with the last six numbers repeating over and over as a set due to the number 7 being in there). But when I did this same 9 divided by 8 divided by 7 and so on on my computer calculator, I got the same number EXCEPT the decimal point came before the first two 2’s, the 142857 was repeated unnecessarily 4 times, followed by the incorrect
142856e-4, I mean the 6 is probably a rounding, and then that e-4. But I don’t feel that this e is the same as when the e occurs after awhile in large calculations and means something to do with the mathematical number e (log). I’m guessing that the 4 means that the decimal point must be moved four places to the left of where the calculator says it is, which would be correct. So am I to suppose that when a number ends in e-something, the rule is to ignore the number before it as a rounding, and move the decimal to the left by as many places as the number after the e says? And a much bigger question: why is there nothing under HELP in this computer calculator that explains this? What if some naive person were trying to use it?
signed: I Hate Rounding and Misleading Calculators
Who said a naive person isn’t trying to use it?
Just kidding. The e stands for exponent, and ~~~e-4 means ~~~*10^(-4), i.e. whatever you have, times ten to the negative four, i.e. whatever you have divided by 1000.
The incorrect final digit is just a round-off error.
In this case, “e” means “exponential notation”, a way of expressing large and small numbers.
For example, the number 1,286,000,000,000 is the same as 1.286 x 10[sup]12[/sup]. In exponential notation this is 1.286E12
Small numbers work the same way. .000000000001286 is 1.286 x 10[sup]-12[/sup] or 1.286E-12
I presume that the calculator help assumed you are familiar with mathematical notation.
The calculator is giving the number is what is called standard notation, which gives the a number between 1 and 10, multiplied by a power of ten, where the power is indicated by the number after the e. In this case. it is 10 to the power of -4, which is 1/10^4 = 1/10000. So, this ends up meaning you move the decimal point the the left 4 places, as you say.
This has nothing to do with the e button on the calculator, by the way, or at least not directly.
As for rounding, it works in the normal way, with the last digit being rounded up if the previous one is 5 or more, or down if less than 5. It’s just that the original number is multiplied (or divided), by 10 so many times to make it between 1 an and 10, before the rounding takes place (and then the appropriate power of 10 is included to get it back to what the number was.
Other people seem to have posted other stuff before me, but this might still be useful.
The rounding in the calculators mey not be correct sometimes, if you look carefully this is an equalty:
log(2^(1/2))=(1/2)log2, but if you solve each one separately, you obtain different results. This is because the calculator doesn’t do rounding eccurately. I believe that the number you obtained (142856) isn’t correct, because it should have been 142857.
By the way (interesting note…, well… at least for me), this number has some properties like:
142857 x 2 = 285714 (the same number rearranged)
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
142857 x 7 = 999999
and it continues like that… you should try some more…
if you’d like better explanation, or are interested in some other stuff like that, i recommend a book from Malba Tahan. i do not know what the exact title is, but is is something like “the man that calculated”
On some calculators, you may encounter a decimal point and the letter E in another situation: when the result of some operation is too big to be displayed.
For example, on an 8-digit calculator, multiplying 12,345,678 * 10 might show the result “1.234567E”. Here the E means Error, and the decimal point shows where the number would be cut off by the left edge of the display–since the actual result is 1,234,567,890, only the ‘23456780’ would fit on the 8-digit display, and the ‘1’ would be pushed off the left side.
Oops. Change “1,234,567,890” to “123,456,780” and my post will make sense.