Floating point numbers core concept

The core concept of floating point numbers is that you take a magnitude (base^exponent) and add it to a fractional of the same magnitude to come up with a resulting number. When coming up with the appropriate magnitude, you choose the highest magnitude you can without exceeding the resulting number. Note that adding a magnitude to itself results in the next higher magnitude, so this covers everything between the 2 magnitude levels.

Some example base 10 magnitudes:
10^-3 = 0.001
10^-2 = 0.01
10^-1 = 0.1
10^0 = 1
10^1 = 10
10^2 = 100
10^3 = 1000

Some example numbers within the above magnitudes
1.00: 1 magnitude * 1.00
1.01: 1 magnitude * 1.01
1.02: 1 magnitude * 1.02

10.00: 10 magnitude * 1.000
10.01: 10 magnitude * 1.001
10.02: 10 magnitude * 1.002

Lets say the mantissa (digits right of the radix point) max out at 3 digits. As seen above that would mean the max precision at 10 magnitude would be 0.01.

100.1: 100 magnitude * 1.001

The higher the magnitude the lower the precision. At 100 magnitude max precision is reduced to 0.1. The mantissa essentially evenly divided the range between 2 magnitudes. In this case it divides it into 1000 evenly spaced levels. If limited to 3 mantissa digits, you can not represent the number 100.01. Though that's in terms of 'absolute precision', 'relative precision' is always maintained, relative precision in this case is always 1/1000 of the magnitude.