that's slightly incoherent and reflective of the same confusion i identified; there is strictly speaking, no such thing as a decimal number, only a decimal numeral. normally the difference is subtle, but in this case it's the essence of the issue
'decimal' means 'base 10'
numbers, the abstract entities we do arithmetic on, are not decimal or in any other base; it is correct that arithmetic on them is not in any sense lossy
decimal is a system of representation that represents these abstract numbers as finite strings of digits; these are called 'numerals'. it can represent any integer, but only some fractions, those whose denominator has no prime factors other than 2 or 5. such fractions arise non-lossily as the result of the arithmetic operator of division when, for example, the dividend is 3. representing these in decimal requires rounding them, so decimal is lossy
binary floating point is lossy in the same way, with the additional limitation to only being able to represent fractions whose denominator is a power of 2, whose numerator does not have too many significant bits (53 most often), and which are not too positive, too negative, or too small
there are other systems of represention for numbers that are not lossy in this way. for example, improper fractions, mixed numbers, finite continued fractions, and decimal augmented with overbar to indicate repeated digits
I think people are speaking shockingly imprecisely in this thread. here's my claim:
> Arithmetic (between two decimal numbers) is clearly not lossy in and of itself, only as implemented with computers
Counterarguments are basically on the level of "you cant represent Pi as a finite decimal number", which I find uninteresting.