How does a computer store real numbers?

Without all the mumbo jumbo, in a nutshell;
Computers store real number using an equation (sum) alot like scientific notation, except without the decimals, basically like this:
378 X 10 4
that 4 is suppose to be tiny, but im hoping y'all know what I mean. This is called floating point, not scientific notation.
the 378 bit would be called the exponent
and the 4 would be called Mantissa
or the other way around, im not sure. The bold Words will be key Words you'll probably need.