In the decimal representation of a positive number $\alpha$, all decimal places starting from the third digit after the decimal point are discarded (i.e., the approximation of $\alpha$ with a deficiency accurate to 0.01 is taken). The resulting number is divided by $\alpha$, and the quotient is again rounded down with the same precision. What numbers can result from this process?
Let $\alpha=n / 100+\alpha_{1}$, where $n-$ is an integer and $0 \leq \alpha_{1}<1$. If $\alpha_{1}>0$, then $\frac{n}{n+100 \alpha_{1}}>1 / 2$, since $100 \alpha_{1}<1$. The fraction $\frac{n}{n+100 \alpha_{1}}$ can take all values from $1 / 2$ to 1. Indeed, let $n=1$. As $\alpha_{1}$ varies from 0 to $1 / 100$, the number $\frac{1}{1+100 \alpha_{1}}$ varies from 1 to $1 / 2$.

## Answer

$0 ; 0.5 ; 0.51 ; \ldots ; 0.99 ; 1$

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