# Value of e?

#### Libby

Hi, just looking into metals and came across silver copper alloy having a density of 9900 - 1.05e4 kg per cubic metre. I have been told me that the value of e is (probably quite randomly) 2.71 and others said that it is an abbreviation for 0, eg. 1,000,000 could be written as 1e6 or 10,000 as 1e4 or whatever...can anyone enlighten me on the proper value of it. My sums just don't seem to be working out. An while i am on the subject why the need; if 1.05e4 = 10,500 then why not just write 10,500. Sorry, don't get it

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#### brewnog

Gold Member
'e' can mean a lot of things, depending on context. It does equal (roughly) 2.71 when you're talking about exponentials (perhaps you'll learn about natural logs soon?), but here this is not the case.

When dealing with large numbers (especially involving powers of ten), it is often used to write standard index form just as you exemplified, especially when using computers. In the case you're talking about, it does indeed mean that your alloy has a density ranging from 9900 to 10500 kg per cubic metre.

#### Libby

that simplifies it, thankyou. am a designer not a physicist unfortunately but sometimes we need to know these things. cheers

#### enigma

Staff Emeritus
Gold Member
Yes,

In the case you're referring to, the 'e' means "times 10 to the"

It's done that way because it's easier to get the information at a glance. This aides things significantly, especially when very large numbers are written.

Which is larger?

10000000000 or 100000000000

you need to count the zeros.

Which is larger?

1e10 or 1e11

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#### Integral

Staff Emeritus
Gold Member
Using e in the context of this thread started with computers and spreadsheets. It is a simple abbreviation for "exponent". Early computers simply did not have the ability to show exponents. So they needed something to replace scientific notation.

Scientific notation was and is necessary since due to the word size limits inherent in computers, it was required to express non integers. So what had been:
$$.123 x 10^4$$ became .123e4, This is easily understood and clearly expressible in the limited fonts of the early computers. It has since become a recognize shorthand in the non computing world.

#### dextercioby

Homework Helper
Where did the "x" go...?Did u mean $$0.123\times 10^{4}$$ or $$0.123\cdot 10^{4}$$...?I think so,but why use the "$x$"...?

Daniel.

#### Integral

Staff Emeritus
Gold Member
just to irritate you Dex!

I doubt that it makes much difference to most.

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