To calculate the value of the expression, we need to evaluate each part separately:

1. **Sum of 1 to 100:**

The sum of the first \( n \) natural numbers is given by the formula:

\[
S_n = \frac{n(n + 1)}{2}
\]

So for the numbers from 1 to 100:

\[
S_{100} = \frac{100 \times 101}{2} = 5050
\]

2. **Fractional expression:**

\[
\left( \frac{1}{2} - \frac{1}{3} - \frac{1}{7} - \frac{1}{9} \right)
\]

Finding a common denominator (which is 126), we have:

\[
\frac{63}{126} - \frac{42}{126} - \frac{18}{126} - \frac{14}{126} = \frac{63 - 42 - 18 - 14}{126} = \frac{-11}{126}
\]

3. **Expression \(63 : 2 - 21 : 3.6\):**

\[
63 \div 2 = 31.5
\]

\[
21 \div 3.6 = 5.8333...
\]

Subtracting these results:

\[
31.5 - 5.8333 \approx 25.6667
\]

4. **Alternating sum from 1 to 100:**

Observing the pattern: \(1 - 2 + 3 - 4 + \ldots + 99 - 100\)

Break it into pairs: \((1-2), (3-4), \ldots, (99-100)\)

Each pair sums to \(-1\), and there are 50 pairs:

\[
50 \times (-1) = -50
\]

5. **Final Calculation:**

\[
5050 \times \left(\frac{-11}{126}\right) \times 25.6667 - 50
\]

Simplifying step-by-step:

First:
\[
5050 \times \frac{-11}{126} = -440.873
\]

Then:
\[
-440.873 \times 25.6667 = -11311.808
\]

Finally:
\[
-11311.808 - 50 = -11361.808
\]

Therefore, the value of the expression is approximately \(-11361.808\).