Question $1$: Write the regular expression for fractional numbers in the scientific notation. In the scientific notation for fractional numbers:

You can have only one or two digits before the decimal point and an optional minus sign before it$.$

You must have one or more digits after the decimal point

Then you will have the caret ${(}^{{?}^{?}})$ character to indicate the starting of the exponent $($that is power of $10)$ of the fraction.

The exponent that follows is an integer, that is$,$ a sequence of one or more digits led by an optional minus sign.

For example: $-{1\mathrm{.}02345}^{{?}^{{?}^{?}}}102$ and ${50\mathrm{.}345}^{{?}^{{?}^{?}}}-23$ are both valid fractional numbers in the scientific notation.

Question $2$: convert the regular expression $(d|)$ into an NFA then convert that NFA into a DFA.