[solved] Do you need all bits to represent a byte?

[Ecumene]

In my “computer technology” class, they’re teaching us basic binary.

I keep seeing this:
00000111₂
being:
111₂

I understand that if you wanted to write a byte “101” and “111” together it would be
00000101₂ 00000111₂

My question is, can you write a byte without having the 0s before the actual “useful” part? Or does it mean something else?

(Excuse me if I’m wrong on something, the only teacher I met was a substitute and only taught us the basics, not binary math or anything. In fact, he sometimes wrote it with all the bits, and sometimes just 4 or five. He was kind of inconsistent…)