If I had a fraction of 5/8 which is equal to 0.625 and I want to convert that to base 2 I get:

0.625(base10)= 0.101(base 2).

I have a couple of questions about this:

What do we call "0.101(base 2)"? It can't be a "decimal value" because it's not decimal (ie, dec=10=base 10).

Should I call this a binary fraction? To me a binary fraction is something like the left hand side of this equation:

101(base2)/1000(base2)=0.101(base2)

But my question is, what is the correct terminology for the right hand side of that equation. (and that is the name of the dot in the right hand side of that equation?)

At school I was told it was a "decimal point" but we only ever considered base 10 when we discussed this.

I have a second, deeper, question relating to binary fractions (or whatever they're called).

I was intrigued to see that 1/10 (base 10) creates an irrational number when represented in base 2.

i.e.
1(base 10)/10(base 10) = 10(base 2)/1010(base 2)

but
0.1 (base 10) = 0.000110011... (base 2)

So, if some fractions can be irrational in one base but rational in another, is it possible to (provably) describe PI (or e, or root2, etc.) as a rational number in any base other than base10?

(edit: clarity)