float vs integer

[johnmerlino]

An integer is 4 bytes on a 32-bit computer. A float is 4 bytes on a 32-bit computer. But a float is required to store more digits than an integer. A float needs to store the oneth's place, the tenth's place, the hundredth's place and so on. That is 10 * 10 * 10 = 1000 and counting extra digits that a float has to store. So how can a float do all this in 4 bytes and yet have all the same positive digits that an integer does?

[JLBorges]

A float does not store every possible value; there is a gap between a particular value it can represent and the next higher value it can represent.

The count of real numbers between 1.0 and 1.0000000001 is infinity.

[Stewbond]

An unsigned integer can store any whole number between 0 and 4294967295.

If you try to store 4294967295 as a float, you get something like: 4.2949673 x 10⁹.

A float is just a way of storing a number in scientific notation (base 2) so you can store very big or very small numbers, but less precision.

1 bit to represent the sign
8 bits to represent the exponent (base 2)
23 bits to represent the number

Check this out:
http://www.h-schmidt.net/FloatConverter/IEEE754.html