Why is 5.93e-56 considered to be close to zero?

Question

I am very poor in math but have recently been studying some math courses, unfortunately they do not explain things well.

I have heard multiple times now that values like 5.93e-56 is very close to 0.

I do not know how this is. Is this not a 5.something value? And thus is it not supposed to be higher than 0?

Can anyone explain? I am specifically talking about when this value shows up as F-value in linear regression results.

Answer 1

$5.93$e$-56$ usually means the number $5.93 \times 10^{-56} = 0.0000000000000000000000000000000000000000000000000000000593,$ which is a positive number and in most every-day contexts is considered to be quite close to zero.

Addendum:

I always find it ironic when an entire question is asked asking about the meaning of a notation which is designed to abbreviate terms. It would have been quicker if the "abbreviated notation" wasn't invented at all - i.e. scientists just used $5.93 \times 10^{-56}$ as opposed to $5.93$e$-56$, rather than us all having to spend time explaining to someone that this is what the notation means...

Answer 2

Scientific notation is used to make very large values and very small values that are out of the scale of normal every day observance manageable.

If we measure everything in miles it's it's easy to talk about distance between the corner of College and Ashby and The campanile on the U.C. Berkeley campus, ($1.09$ miles), between San Francisco and Sacramento, Ca. ($87.9$ miles), Between Chicago and Madrid ($4176$ miles) and even the distance between the earth and the sun ($91409000$ miles).

But for large numbers: The distance between Earth and the Alpha Centauri ($25672000000000$ miles) or to the Andromeda galaxy ($14914073000000000000$ miles) or very small numbers. the size of a water molecule ($0.00000000000016777$ miles) things get.... awkward.

But we can make them manageable by considering them in terms of powers of $10$.

So width of a water molecule is $1.6777 \times 10^{-13}$ miles and the distance from college and ashby to the campanile is $1.09 \times 10^0$ miles; between San Francisco and Sacremento $8.79 \times 10^1$; Chicago to Madrid $4.176\times 10^3$ miles; between Earth and Sun $9.1409\times 10^7$; between earth and alpha centauri $2.5672\times 10^{13}$ and earth and andromeda $1.4914073\times 10^{19}$.

Now we have a way to refer to numbers from a wide range of scales.

Scientific notation: We write $a.bc e{number}$ to mean $a.bc \times 10^{number}$.

So $5.93e-56 = 5.93\times 10^{-56} = 0.00000000000000000000000000000000000000000000000000000000593$.

Which is according to most people "very close to zero". Of course, a mathematician must ask "very close to zero in comparison to what".

(To which the answer "compared to $1$" will usually suffice. Except a mathematician might then ask "close on what scale" in which case "within $\frac 1{100000000000000000000000000000000000000000000000000000000}$ of the original" is an acceptable answer.)

(I think most people will concede that "$\frac {593}{100000000000000000000000000000000000000000000000000000000}$ is a very small number and close to $0$" to not be an unacceptable statement.)

.........

"And thus is it not supposed to be higher than 0?"

I'm a bit confused. A number can be higher than $0$ and still be close to $0$ can't it. "very close to $0$" doesn't mean less than $0$, does it?