Loss of numerical precision

The first expression for \( f(x) \) results in $$ f(x)=\frac{1-0.99998}{0.69999\times 10^{-2}}=\frac{0.2\times 10^{-4}}{0.69999\times 10^{-2}}=0.28572\times 10^{-2}, $$ while the second expression results in $$ f(x)=\frac{0.69999\times 10^{-2}}{1+0.99998}= \frac{0.69999\times 10^{-2}}{1.99998}=0.35000\times 10^{-2}, $$ which is also the exact result. In the first expression, due to our choice of precision, we have only one relevant digit in the numerator, after the subtraction. This leads to a loss of precision and a wrong result due to a cancellation of two nearly equal numbers. If we had chosen a precision of six leading digits, both expressions yield the same answer.