Exercises: addition and subtraction of decimal numbers

We consider the following sum: $1 + 0.1 + 0.01 + 0.001 + \dots$

(Perhaps you already know that $0. 2 = \frac{2}{9}, 0. 3 = \frac{3}{9} = \frac{1}{3}, 0. 7 = \frac{7}{9}$ and so on.)

What are the three next terms in the sum after $0.001$ ? How are two successive summands related to each other?
For this task you need the following basic knowledge: Decimal Numbers
The next three terms are:
$0.0001$
$0.00001$
$0.000001$
Each summand is a tenth of its predecessor.
Calculate the value of the above sum both as a repeating decimal and as a fraction.

For this task you need the following basic knowledge: Decimal Numbers
$\to$ Since each additional summand is a tenth of its predecessor, the result must be $1. 1$ .
$1. \underset{tenth}{\overset{+ 0.1}{1}} \underset{hundredths}{\overset{+ 0.01}{1}} \underset{thousandths}{\overset{+ 0.001}{1}} and so on.$
$\frac{10}{9}$ is the fraction corresponding to $1. 1$ .
Calculate the value of the difference $3 - 0.2 - 0.02 - 0.002 - \dots$ both as a repeating decimal and as a fraction.

For this task you need the following basic knowledge: Decimal Numbers
$\to$ Since each subtracted term is a tenth of its predecessor, the result must be $3 - 0. 2$ .
$\frac{25}{9}$ is the fraction corresponding to $3 - 0. 2$ .

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