Question

Which is bigger 0.01 or 0.009999999999999

Answer 1

Answer:

They might be equal actually

Explanation:

Well $0.01$ is actually bigger if we don't see $0.009999999999999$ as $0.00\overline9$ as $0.00\overline9$ and $0.01$ are actually equal. However your questionnaire might mean $0.009999999999999$ as $0.00\overline9$ so you might want to clarify that with your teacher.

Proof of $\bold{0.01 = 0.00\overline9}$:

We let $x = 0.00\overline9$

$x = 0.00\overline9 \\ x \times 10 = 0.00\overline9 \times 10 \\ 10x = 0.09\overline9 \\ 10x -x = 0.09\overline9 - 0.00\overline9 \\ 9x = 0.09 \\ \frac{9x}{9} = \frac{0.09}{9} \\ x = 0.01$