Numbers between decimal number

Question

So there is a question that says I can choose a number between $0.00001$ and $0.1$, but the problem is what exactly comes after $0.00001$?

Would it be $0.0001$, continued by $0.001$, $0.01$, $0.1$?

or

$0.00002,0.00003,0.00004,...$

I'm really confused :)

Answer 1

There is no “next number” after a given real number because there is always another number between any two real numbers.

For example, the average of two numbers is always strictly between them.

Answer 2

Not only the real numbers , even the rational numbers form a dense set, that means that , given rational numbers $\ a,b\ $ with $\ a<b\ $ , there are infinite many rational numbers $\ c\ $ with $\ a<c<b\ $. You can , for example , choose $$c:=a+\frac{b-a}{k}$$ with some integer $\ k>1\ $ doing the job and already showing the existence of infinite many $\ c's\ $.