Introduction:
The moment of inertia of a system of particles is a measure of the resistance of the system to rotational motion. It depends on both the mass and distribution of particles in the system. In this problem, we are given the masses and positions of four particles on a meter scale, and we need to find the moment of inertia of the system about a perpendicular bisector of the meter scale.

Procedure:
To calculate the moment of inertia of the system, we can use the formula:

I = Σmr²

where I is the moment of inertia, Σ represents the sum, m is the mass of each particle, and r is the perpendicular distance of each particle from the axis of rotation.

Calculating the moment of inertia:
Let's calculate the moment of inertia for each particle and then find the total moment of inertia of the system.

1. Particle with mass 1g at 1cm:
- Mass (m₁) = 1g = 0.001kg
- Distance from the axis (r₁) = 1cm = 0.01m
- Moment of inertia (I₁) = m₁r₁² = 0.001 * (0.01)² = 0.000001 kgm²

2. Particle with mass 2g at 2cm:
- Mass (m₂) = 2g = 0.002kg
- Distance from the axis (r₂) = 2cm = 0.02m
- Moment of inertia (I₂) = m₂r₂² = 0.002 * (0.02)² = 0.0000024 kgm²

3. Particle with mass 3g at 3cm:
- Mass (m₃) = 3g = 0.003kg
- Distance from the axis (r₃) = 3cm = 0.03m
- Moment of inertia (I₃) = m₃r₃² = 0.003 * (0.03)² = 0.0000081 kgm²

4. Particle with mass 100g at 100cm:
- Mass (m₄) = 100g = 0.1kg
- Distance from the axis (r₄) = 100cm = 1m
- Moment of inertia (I₄) = m₄r₄² = 0.1 * (1)² = 0.1 kgm²

Total moment of inertia:
To find the total moment of inertia of the system, we sum up the individual moments of inertia:

I_total = I₁ + I₂ + I₃ + I₄
= 0.000001 + 0.0000024 + 0.0000081 + 0.1
= 0.1000115 kgm²

Conclusion:
The moment of inertia of the system of particles about the perpendicular bisector of the meter scale is approximately 0.1000115 kgm². This value represents the resistance of the system to rotational motion and depends on the mass and distribution of particles in the system.