if 0.9 \overline{7} is written as a common fraction a/b, what is the value of a - b?

here is the decimal \(0.9 \overline{7}\)

This is written as \(9\frac{7}{9} \cdot \frac{1}{10}\)

which equals to \(\frac{44}{45}\)

as the question asks

\(44-45={\boxed{-1}}\)