Fractions and decimals on the number line

Every fraction has a place on the number line. To find $\displaystyle \frac{3}{5}$: cut the segment from 0 to 1 into 5 equal parts, and count 3 parts from 0.

For decimals, cut the segment from 0 to 1 into 10 parts – tenths. $\displaystyle 0.35$ is between $\displaystyle 0.3$ and $\displaystyle 0.4$. Zoom in there and cut into 10 again – hundredths: $\displaystyle 0.35$ is exactly halfway.

$\displaystyle 3\frac{1}{5}$ is between 3 and 4: from 3, one fifth of the way to 4.

Zoom in between $\displaystyle 0.5$ and $\displaystyle 0.6$: cut it into 10 parts, and there are $\displaystyle 0.51$, $\displaystyle 0.52$ … $\displaystyle 0.59$. Zoom in again between two of them, and there are more. Between any two numbers there is always another number – as many as you like.

Draw a segment from 0 to 1 and place on it, roughly, $\displaystyle \frac{5}{6}$ and $\displaystyle 0.35$.

Place, roughly, $\displaystyle 0.72$, $\displaystyle 0.27$, $\displaystyle 0.027$ and $\displaystyle 0.270$ on a number line.
Two of them fall on the same point – which, and why?

Find three numbers between $\displaystyle 0.11$ and $\displaystyle 0.12$.
How many such numbers are there, do you think?