Why can floating point store more values than integers?

Question

In a 32-bit floating point, it was said that the highest possible value is 3.4028235 x 10^38. However, when we evaluate this, it will be equal to 340282346638528860000000000000000000000. This whole number would require more than 100 integer bits right? My question is: If that is the case, how come this number requiring more than 100 bits fitted in a 32-bit floating point?

In: 3

Answer 1

A 32-bit float can actually store fewer values than a 32-bit integer. The floating point values cover a much larger range but many of the possible values are exactly equal to other values. Most obviously, floating point has negative zero.