The foregoing is one of the reasons why COBOL (and other languages, as well) implemented binary coded decimal (BCD) arithmetic.   When numbers are expressed in this way, a base-10 number is literally base-10, with both the digits and the sign being expressed by groups of (usually) 4 or 8 bits.   The arithmetic is performed in base-10 to a definite (and fixed) precision.   Every modern microprocessor has hardware-level support for it.

In fact, in COBOL, the default is always to perform decimal arithmetic, unless the COMP[UTATIONAL] directive is specified.

Another strategy, used e.g. by Microsoft Access and its JET database engine, is scaled integers.   The Currency data type in that system is implemented by a true binary integer whose value is assumed to be multiplied by 10,000.   This gives accurate, base-10-float compatible operations with exactly 4 digits of fixed precision, without actually using floating-point.