(Calculus Review: ) How many real numbers lie between 0.0 and 0.0625?
An infinite number.
The limited precision of fixed point (and floating point) expressions
is a problem for programmers.
Even with 64-bit double precision floating point
(such as Java data type double) precision is limited.
Only 264 numbers can be represented.
This is a lot, but between
any two numbers that are represented there are an infinite number of
real numbers that are not represented!
(If your calculus is a little vague, don't worry. Just think about the nearly infinite number of atoms between any two marks on even the most precise ruler.)
How many digits does the value pi have?