explain why some numerical values have an unlimited number of significant digits

3 answers

Those numbers that are "defined" numbers for conversions; i.e., 12 inches in 1 foot or 3 feet = 1 yard are unlimited. There are 12.0000000etc inches in 1 foot because that's the way it is defined. Another case is if we say there are 100 people in a particular room, then that is 100.000000etc because we can't very well take 100.01 or 99.99 persons.
Perhaps this means irrational numbers, for example pi = 3.14159 etc
or e = 2.718281828 etc
that is my guess anyway.
Oh, Dr Bob knows this far better than I