Regular expression and Right Regular grammar for decimals starting with 1 ending with 9?
Your regular expression is correct, however, your grammar isn't. Assuming $E = \varepsilon$, you can derive words like $S \to \mathtt{1}\,X \to \mathtt{1}\,\varepsilon = \mathtt{1}$.

A right regular grammar might look like this:
\begin{align}
S &amp;::= \mathtt{1}\,A\\
A &amp;::= \mathtt{0}\,A \mid \mathtt{1}\,A \mid \mathtt{2}\,A \mid \mathtt{9}\,A \mid B\\
B &amp;::= \mathtt{.}\,C\\
C &amp;::= \mathtt{0}\,C \mid \mathtt{1}\,C \mid \mathtt{2}\,C \mid \mathtt{9}\,C \mid D\\
D &amp;::= \mathtt{9}
\end{align}