What does E mean on a calculator?
Short answer. On a display, E means "times ten to the power of". So 1.2E8 is 120,000,000 and 3.5E-4 is 0.00035. The exponent says how many places to move the decimal point: right if positive, left if negative. A lowercase e on a key is different. That is the constant 2.71828.
Two different things wear the letter E on a calculator, which is why the question keeps getting asked. One is a piece of punctuation for very large and very small numbers. The other is a mathematical constant. They have nothing to do with each other.
The E in a result is a power of ten
When a number is too long for the display, the calculator stops writing digits and writes the size of the number instead. E is shorthand for times ten to the power of, and the number after it is the exponent:
1.2E8 means 1.2 × 10⁸ = 120000000 3.5E-4 means 3.5 × 10⁻⁴ = 0.00035
This is called scientific notation, or sometimes E notation when it is typed on one line. The E exists purely because a screen cannot show a raised exponent.
Reading it: move the decimal point
The exponent counts places, not zeros. Put your finger on the decimal point and walk it that many steps. Positive walks right and makes the number bigger. Negative walks left and makes it smaller.
4.07E5 4.07 → 40.7 → 407 → 4070 → 40700 → 407000
five steps right
6.5E-3 6.5 → 0.65 → 0.065 → 0.0065
three steps left
A quick sanity check: the digits never change, only their position. If your answer has different digits in it, you moved something you should not have.
| Display | Means | Written out |
|---|---|---|
1.2E8 | 1.2 × 10⁸ | 120,000,000 |
2E13 | 2 × 10¹³ | 20,000,000,000,000 |
4.07E5 | 4.07 × 10⁵ | 407,000 |
6.5E-3 | 6.5 × 10⁻³ | 0.0065 |
3.5E-4 | 3.5 × 10⁻⁴ | 0.00035 |
1.25E-7 | 1.25 × 10⁻⁷ | 0.000000125 |
Why the display switched to E without asking
Because the answer outgrew the screen. An eight digit display can hold 99,999,999 and not one more, so the moment a result crosses that line it has to be described rather than spelled out:
5000000 × 4000000 = 20000000000000 14 digits, shown as 2E13 1 ÷ 8000000 = 0.000000125 shown as 1.25E-7 2³⁰ = 1073741824 10 digits, shown as 1.073741824E9
Nothing has gone wrong. E is the calculator being honest about running out of room. The same thing happens at the small end, where leading zeros would eat the whole display before a single meaningful digit appeared.
Typing an exponent yourself
You do not type the letter. There is a dedicated key, labelled EE, EXP or ×10ˣ depending on the calculator, and it means "and now here comes the exponent". To enter 1.2E8 you press 1.2, then that key, then 8. Three keystrokes instead of nine.
The common mistake is pressing the multiply key as well, as in 1.2 × EE 8. That gives you an extra factor of ten and an answer ten times too big. The exponent key already contains the multiplication.
The other e: 2.718281828459045
A lowercase e printed on a key, usually beside e^x or near ln, is Euler's number. It is a fixed constant, roughly 2.71828, and it is the base of natural logarithms. It is not punctuation and it never appears in the middle of a result the way display E does.
Where it comes from is worth thirty seconds. Compound interest on 1 unit at 100% a year, split into ever finer intervals, does not run away to infinity. It creeps toward a ceiling:
12 times a year (1 + 1/12)¹² = 2.61304 365 times a year (1 + 1/365)³⁶⁵ = 2.71457 a million times (1 + 1/1000000)¹⁰⁰⁰⁰⁰⁰ = 2.71828 the ceiling itself e = 2.718281828459045...
That ceiling is e. It turns up anywhere growth feeds on itself, which is why calculators give it a key. And because ln is the logarithm to base e, ln(e) is exactly 1, a handy way to check which e your calculator means.
When E means neither of those
On some basic calculators a lone E, with no digits attached, is an error flag: division by zero, or a result too big even for E notation. If the E stands alone rather than sitting between a number and an exponent, it is a complaint, not a value. Clear and try again.
The digits E does not show you
E notation is a display format, and display formats round. A calculator that shows six significant figures reports 2³⁰ as 1.07374E9, which written out is 1,073,740,000. The true value is 1,073,741,824. The screen quietly dropped 1,824.
Usually that is exactly what you want, since nobody needs fourteen digits of a lab measurement. It matters when the rounded number goes back into another calculation and the error compounds, which is the same failure that makes 0.1 + 0.2 come out as 0.30000000000000004 on most machines. A calculator that keeps the exact value internally and only rounds for the screen will hand you back the full 1,073,741,824 the moment there is room to print it. One that rounds first has thrown those digits away for good. Prism computes exactly, so 0.1 + 0.2 is 0.3, and what E hides is still there underneath.
Percent error is the usual way to say how much that rounding cost you, if you need to put a number on it: see the percent error formula.
Scientific mode, with the exponent key where you expect it
Prism has EE for entering exponents, e^x and ln for the constant, and it does not round your answer before you have seen it. Scientific mode is free forever, no subscription. See the app.