5Exercise: Recurring decimal numbers

The following sum occurs: $1+0.1+0.01+0.001+\dots$

Think about: $0.\overline{2}=\frac{2}{9},\ 0.\overline{3}=\frac{3}{9}=\frac{1}{3},\ 0.\overline{7}=\frac{7}{9},\ \text{and so on}$

1. Write the three successors of the summand 0.001. Describe how the sum is built up.

2. Calculate the value of the above sum.

3. Calculate: $3-0.2-0.02-0.002-...$