Units, Dimensions and Errors: One-Page Formula Sheet

Units, Dimensions and Errors — formula sheet

Formulas

• If Z = AᵖBᵠ/Cʳ, then ΔZ/Z = p·ΔA/A + q·ΔB/B + r·ΔC/C
• Absolute error in a sum or difference: ΔZ = ΔA + ΔB
• Vernier reading = MSR + VSR × least count
• Screw gauge least count = pitch ÷ number of circular divisions

Key ideas

• SI base units: kg, m, s, A, K, mol, cd
• Only like dimensions can be added or compared
• Dimensional method cannot find dimensionless constants (like 2π)
• Significant figures and least count decide reported precision

Traps to avoid

• Subtracting errors for a difference (errors always add)
• Forgetting zero error in vernier and screw gauge
• Treating angle as dimensional (radian is dimensionless)

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