We are looking at proportions/ equivalent fractions here, lets compare the fractions;
[tex]\begin{gathered} \frac{k}{100}=\frac{1}{10} \\ \text{cross multiply, we have} \\ 10k=100 \\ \text{divide both sides by 10} \\ \frac{10k}{10}=\frac{100}{10} \\ k=10 \end{gathered}[/tex]Therefore, the number that could replace k is 10.