You can write both numbers as fractions:
[tex]6.3=\dfrac{63}{10},\quad 0.9=\dfrac{9}{10}[/tex]
Dividing by a fraction is the same as multiplying by its inverse, so we have
[tex]\dfrac{63}{10}\div \dfrac{9}{10}=\dfrac{63}{10}\cdot\dfrac{10}{9}[/tex]
We can cross-simplify the 10's and we have
[tex]\dfrac{63}{10}\cdot\dfrac{10}{9}=\dfrac{63}{9}=7[/tex]
