# What does the ‘e’ mean on a calculator’s answer?

• What does the ‘e’ mean on a calculator’s answer?

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You are about to get very confused because e has two meanings. The most common is e in math –

The number e is a mathematical constant that is the base of the : the unique number whose natural logarithm is equal to one. It is approximately equal to 2.7182. That is not the normal calculator usage.

One of my first calculator was the TI SR10 that could use scientific notation. Our calculators are trying to display the number using scientific notation. My calculator would use the capital E instead of the lower case e. I have not seen the lower case ”e” used. Scientific notation shows a number with a decimal, a fractional decimal portion times 10 raised to an exponent. In your case it is trying to say 20000000000, but it can’t write an exponent and put in a x10, that would be awkward and confusing. I am not 100% sure of the origins for the calculator’s use of E or e, but it sure looks like they lifted it from the FORTRAN programing language because FORTRAN and even BASIC used similar type output nomenclature and predates the calculator. You can think of it as meaning TIMES EXPONENT OF TEN. So just adjust your decimal point, to the right for positive numbers and left for negative numbers. This notation is what we lived with when we used real slide rules.

“What does the ‘e’ mean on a calculator’s answer?”

Two totally different things:

a) In the keyboard section, as well as on the answer left of the ‘=’ sign, ‘e’ means the constant number e = 2,71828182845 . . . (approximate decimal representation), also called Euler’s Number, which is the base of the Natural (or Neperian) logarithms, chosen for that role because it alone, of all the real numbers, has the property that the function f(x) = eˣ has itself as its derivatives.

f’=f, f’’=f, f’’’=f . . . ad infinitum.

b) On the answer, right of the ‘=’ sign and directly behind some digits, ‘e’ is nothing but a shorthand for “exponent of ten”, when very big or very small numbers would require too many zeroes for their representation. So, in the example given,

5.5555853e+15 means 5.5555853*10^(+15), but

e^(-30)=9.357623e-14 means e^(-30)=9.357623*10^(-14).

Don’t get confused!

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As you know from reading other answers, that E stands for the “exponent” in the ×10ⁿ part of scientific notation.

Your number, 2E10 is equal to 2×1010

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$2×{10}^{10}$

If you want to write this number in normal number form, just move the invisible decimal point to the right, adding zeroes as necessary.

• 2→0→0→0→0→0→0→0→0→0→0
• 20,000,000,000

If your number was 2E-10, that would be 2×1010

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$2×{10}^{-10}$

and you would turn the decimal point visible and move it ten places to the left, adding zeroes as necessary.

• 0.0000000002

.

Original Question:

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Mathematically, it means “times 10 to the power of” So 5.55e+15 is equivalent to 5.55 X 10 ^ +15.

Informally, the number after the “e” tells you how many digits long the number is. So 5.55e+15 is 15 digits long. (5,555,585,300,000,000)

For example, 2e+6 would be a 2 followed by 6 zeros (2,000,000).

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That is a form to write of numbers.

So for example instead of saying 51015

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$5\ast {10}^{15}$

(5 followed by 15 zeros) you use that notation, 5e+15, which means the same thing.

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The ‘e’ is there because the answer is too large to show on the limited digits of the calculator’s screen. The number after the ‘+’ sign represents the power of ten by which to multiply the first number on the screen.

The calculator is telling you that the full number is 5.5555853 x [10 to the power of 15].

In this case, the answer has 15 digits.

A simple way of realizing this answer is to move the decimal place to the right by 15 numbers. If the answer were 5.5555853e+3, the answer would be 5555.5853.

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It’s short for exponent. It’s a representation of the “scientific” notation for very large or small numbers, which writes these as a product of a power of 10 and a number between one and ten. Thus:

5.5555853e+15 = 5.5555853 x 10^15

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If it gave the answer 2(10^10), I could tell you. Not all calculators are the same. I am not sure whether it means:

1. 2^10 :: “e” would stand for exponent
2. 2(e^10) :: where “e” is 2.7etc. (the “e” from from natural logs)

Put in some calculation that you know the answer. You can figure it out for yourself.

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It’s a more compact representation of scientific notation. The mantissa is given as the number before the ‘e’, and the exponent after the ‘e’. Your example would be the equivalent of:

5.5555853 x 10^15

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