In other words, a floating point number consists of 2 numbers and a sign bit:

1. the digits

2. the exponent

3. a sign bit

If you're familiar with scientific notation, yes, it's the same thing.

https://en.wikipedia.org/wiki/Scientific_notation

The rest is just the inevitable consequences of that.

I like "decimal point position" more than "exponent". Also, if I remember correctly, "mantissa" is the significand (the digits of the number).

And by the way engineering notation (where exponent must divide by 3) is so much better. I hate converting things like 2.234·10¹¹ into billions in my head.

And by the way (unrelated to floating point) mathematicians could make better names for things, for example instead of "numerator" and "denominator" they could use "upper" and "lower number". So much easier!