GATE CSE 2026 Session 2 Q64: Discontinuities of a function of the second decimal digit

Consider a function $f: (0,1) \rightarrow \{0, 1\}$ defined as follows.

For a real number $r \in (0,1)$, $f(r) = 1$ if the second digit after the decimal point in $r$ is one of the four digits 2, 3, 6 and 7. Otherwise, $f(r)$ is equal to 0.

The number of points in $(0,1)$ at which $f$ is discontinuous is ___________. (answer in integer)