I was looking at these two numbers the other day:

$0.01$

$\frac{5764607523034235}{576460752303423488}$

It turns out they are very close, differing only by about 5 parts in a quadrillion.

A tech support case caught my attention on that day because MATLAB creator Cleve Moler (Numerical Computing with MATLAB, Experiments with MATLAB, Cleve's Laboratory, Cleve's Corner) responded to it, and I always enjoy Cleve's explanations.

The tech support case turned out to be related to understanding how floating-point numbers work. In part of his response, Cleve said, "1.e-2 is not one-hundredth; it is the floating point number