【Analysis】A simplest fraction, if it can be simplified to a simplest fraction, then its denominator can only contain prime factors $2$ and $5$. Fractions with a two-digit denominator and a numerator of 1 are clearly simplest fractions.  
Therefore, the denominator of these fractions, when factored into prime factors, should be in the form of $2^{a} \times 5^{b}$.  
1. When $b=0$, $a$ can take values from 4 to 6, for a total of 3 possibilities.  
2. When $b=1$, $a$ can take values from 1 to 4, for a total of 4 possibilities.  
3. When $b=2$, $a$ can take values from 0 to 1, for a total of 2 possibilities.  
When $b \geq 3$, $2^{a} \times 5^{b} \geq 5^{3} > 99$  
In summary, there are $3+4+2=9$ such fractions.
7、The denominator is a two-digit number, the numerator is 1, and the fraction can be converted into a finite decimal. There are $\qquad$

The fraction has a two-digit denominator, a numerator of 1, and can be converted into a finite decimal. There are $\qquad$