In this case, there are two mechanisms at work: a conventional rounding bit (for each of the two floating point accumulators available), and a special routine,

In this case, there are two mechanisms at work: a conventional rounding bit (for each of the two floating point accumulators available), and a special routine, which zeros out all bytes of the floating point accumulator, when the result is transferred and the exponent is zero. I personally suspect that it's the latter, which is not triggered appropriately and which seems to be the culprit here. Notably, this routine only applies to the first of these accumulators. (It seems, though, that the routine should be called, when a value is copied from one FAC to the other, which we would expect here to happen. So I'm not sure.) (The precision, BTW, is 4 bytes mantissa including a sign bit, and one byte exponent with a bias of 127. The floating point accumulators extract the sign to an extra byte, but there is no change in precision with regard to the storage format, other than said rounding bit. At least, this is what it's in Commodore BASIC, the flavor I'm most familiar with. Apple ][ BASIC should be pretty much the same, as it's closely related. And, notably, the 6502 processor only provides addition and subtraction for single-byte values, everything else has to be done in software. So there's no extra precision in any processor register, either.)