[ Decimal fractions]

How are the decimal representations of the numbers $\left\{\frac{p}{q}\right\}$ and $\left\{\frac{10^{k} p}{q}\right\}$ related?

## Answer

If $\left\{\frac{p}{q}\right\}=0, a_{1} a_{2} \ldots a_{k} a_{k+1} \cdots, \quad$ then $\left\{\frac{10^{k} p}{q}\right\}=0, a_{k+1} \cdots$

Find the possible values of the denominator of a common fraction of the form ${ }^{1 /}$, which is represented by a purely periodic decimal fraction with two digits in the period.
According to problem $\underline{60876}$, these are the divisors of the number 99 that are not divisors of the number 9.

## Answer

$11,33,99$.