In grade school and high school, I was taught a real number is a number with a decimal expansion--that is, a finite sequence of digits followed by a decimal point followed by an infinite sequence of digits.
When I moved on to studying analysis, I was introduced to the Dedekind cut construction of the real numbers, and then proved every real number could be expressed as a decimal expansion.
Now presumably, the real numbers could also be rigorously constructed as decimal expansions, very similarly to the Cauchy sequence construction.
Is there a particular reason why, when Dedekind performed his original construction of the reals, he chose to use cuts rather than decimal expansions (or base 2 expansions for that matter)? Is there some unforeseen difficulty in rigorously constructing the reals by means of decimal expansions?