ELI5-What does the ‘e’ in large calculations mean, and why does it only appear in a calculator and not when one actually solves problems?
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Can you give an example?
E is a term in scientific notation saying that the actual value is many powers of 10 greater or lesser.
Instead of writing 8,120,000,000, we write 8.12 x 10^9, or 8.12e9.
Instead of writing 0.000037, we write 3.7 x 10^-5, or 3.7e-5.
Something like 2e10?
That’s scientific notation. It’s basically a compressed way to write long numbers. You can think of the number after e as “how many zeroes am I adding to the end of this”. So 2e10 would be 20000000000. Sometimes you’ll see it with a decimal point(like 2.53e10). In that case, you would take the 53 as the first two zeroes and put down the other 8 at the end, so you would get 25300000000.
I think you’re referring to the scientific notation “E.” Like if you make a large calculation and get a number like 4.566 E8. The E in this case is shorthand for “times ten to the power of…” and then the next number. So it’s showing that the number is in scientific notation, which is a handy way to represent large numbers.
So my example of 4.566 E8 would be 4.566 x 10^(8) in scientific notation, replacing E8 with “x 10^(8)”. And both of those would be 456,600,000 if we were to write it out normally. Especially on older calculators that could only show limited digits, this was an easier way to show big numbers.
The e is just a representation. The calculator solves things into scientific notation. Basically, scientific notation just shortens a number by multiplying by 10 to the power of x. For example, nine hundred thousand (900,000) in scientific notation would be 9×10^5. In really simple terms, its just how many “zeroes” after the decimal, since you are multiplying by 10. A calculator would read that as 9e5. Its not a variable so its not in any math equation, it just represents a number. People just write out 9×10^5 because e looks like a variable or eulers number.
It is short for “exponent” or “exponential form”. It appear in calculators because it is easier to display 1.9773e30 than 1.9773*10^(30) which is the *proper* way to write it. You save two characters by replacing the whole *10 with just the ‘e’ *and* don’t need to bother with a method of displaying superscript. It only exists because calculator manufacturers are cheap.
The calculator has a fixed number of digits, and more digits would mean more LEDs or LCDs and cost more money.
Let’s say your calculator has 8 digits. It can display 12,345,678 with no problem. But what if you mulitply that by 9? The answer is 111,111,102; but the biggest number the calculator can display is 99,999,999.
There are two choices, A) no answer or B) find a better way to show 111,111,102. Calculators take choice B because choice A isn’t useful. It shows 1.11111e8. This isn’t the whole answer, only 6 of 9 digits, but the scientific notation tells you the calculators best representation is 1.11111 x 10^8 for 111,111,000. It’s not exact, but pretty close.
Just something to add, ‘E’ and ‘e’ can be used close to each other for wildly different things.
The other comments have explained how E is often used in calculators for scientific notation, where it is easier and cheaper to display 1.2E12 than 1.2 x 10^(12) or 1 200 000 000 000.
It is also possible you’ve seen *e*^(x) as a button on the calculator. This is simply a quick function for taking the input number and raising *e* to its exponent; in other words, if you type in ‘5’ and then press the *e*^(x) button you’ll get the result of *e*^(5). *e* in this case is [Euler’s Number](https://en.wikipedia.org/wiki/E_(mathematical_constant)) and is used often with continuous interest and a surprising amount of other things, which is why it has a special button.
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