They might be equal actually
Well [tex]0.01[/tex] is actually bigger if we don't see [tex]0.009999999999999[/tex] as [tex]0.00\overline9[/tex] as [tex]0.00\overline9[/tex] and [tex]0.01[/tex] are actually equal. However your questionnaire might mean [tex]0.009999999999999[/tex] as [tex]0.00\overline9[/tex] so you might want to clarify that with your teacher.
Proof of [tex]\bold{0.01 = 0.00\overline9}[/tex]:
We let [tex]x = 0.00\overline9[/tex]
[tex]x = 0.00\overline9 \\ x \times 10 = 0.00\overline9 \times 10 \\ 10x = 0.09\overline9 \\ 10x -x = 0.09\overline9 - 0.00\overline9 \\ 9x = 0.09 \\ \frac{9x}{9} = \frac{0.09}{9} \\ x = 0.01[/tex]
