The Uncountable Set of Decimal Numbers

There's this remarkable point that there can be sets that are not countable and I guess maybe the simplest example would be think of a line that goes off to infinity in both directions. The first surprising thing is that those sets that seem to be larger than the natural numbers actually are the same size as the natural numbers they're countable. But then there's the other surprise which is that the real numbers the set of decimal numbers are uncountable.