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$$\frac{0.314^5}{120}=2.5437065e\!−\!5$$

I did this calculation by my android phone's calculator.

I can't understand the result I got (The RHS of calculation).

Please help. What is this?

Bill Dubuque
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Akash
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  • note that what appears as an em-dash with padding here in MathJax, really is a simple minus sign on the device. This way it looks like e times the factor, minus five. In engineering notation, there are no spaces between e, minus and exponent. – dlatikay Oct 21 '18 at 15:55

3 Answers3

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phone calculators often use this input for large or small numbers. In this context: $$'e-5'=10^{-5}$$ so your answer is: $$2.5437065\times10^{-5}$$

Henry Lee
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$2.5437065e−5$ is really $2.543706 \times 10^{−5} = 0.00002543706$.

(I haven't checked the arithmetic.)

Ethan Bolker
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It seems that this is your first encounter with the so-called scientific notation.

For very large or very small numbers, you need many digits but only the first significant ones are useful. Hence you shift the decimal point after the first digit and compensate by multiplying by a suitable power of ten.

E.g.

$$2573475675632465243747463476727\approx2.57347\times10^{30}$$

$$0.000000000000052352344643\approx 5.23523\times 10^{-14}.$$

$e\,n$ or $E\,n$ is used as an abbreviation of $\times10^{n}$ (for exponent). This is legacy from the first scientific programming languages.

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    In this calculation the numerical answer is in fact exact. I think scientific notation with "e" in the display is for typographical reasons - perhaps the field is too short, and superscripts are unavailable. – Ethan Bolker Oct 21 '18 at 13:55
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    @EthanBolker: I said that this is legacy from the old days. Superscripts were out of question and E is shorter than x10^. If I am right, usage of lowercase e was later popularized by the C language. –  Oct 21 '18 at 13:57