Diagram 1: Error Propagation Decision Tree
Z = f(A, B, C)?
Operation
type?
+ or −
Add ABSOLUTE
$\Delta Z$ = $\Delta A$ + $\Delta B$
× or ÷
Add RELATIVE
$\Delta Z$/Z = $\Delta A$/A + $\Delta B$/B
Aⁿ
Multiply by POWER
$\Delta Z$/Z = n · ($\Delta A$/A)
Errors NEVER subtract — always add
(worst-case / maximum error)
Diagram 2: Dimensional Formula Comparison
Quantities Sharing Same Dimensions
[$M^{1}$$L^{-1}$$T^{-2}$]
• Pressure
• Stress
• Young's Modulus
• Energy Density
[$M^{1}$$L^{2}$$T^{-2}$]
• Kinetic Energy
• Potential Energy
• Work Done
• Torque (τ)
[$M^{1}$$L^{1}$$T^{-2}$]
• Force (F = ma)
• Weight
• Tension
[$M^{1}$$L^{2}$$T^{-1}$]
• Angular Momentum
• Planck's constant (h)
• Action (S = ∫L dt)
⚠ Same dimensions ≠ same physical quantity
Key Numerical Table: G Conversion Step-by-Step
| Step | Operation | Value |
|---|
| G in SI | Given | 6.67×10−1^{1} N m2 kg−2 |
| Dimensional formula of G | [M^{-1}$$L^{3}$$T^{-2}] | a=−1, b=3, c=−2 |
| Mass conversion | (1 kg / 1 g)^{-1} = (10^{3})^{-1} | × 10^{-3} |
| Length conversion | (1 m / 1 cm)^{3} = (10^{2})^{3} | × 10^{6} |
| Time conversion | (1 s / 1 s)^{-2} | × 1 |
| G in CGS | 6.67×10−1^{1} × 10^{3} | 6.67×10−8 dyne cm2 g−2 |
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