Types of Errors:

1. Systematic: Consistent bias (zero error, calibration). Cannot be reduced by averaging.
2. Random: Unpredictable scatter. Reduced by multiple readings and averaging.
3. Gross: Mistakes in reading/recording. Eliminated by careful practice.

Error Measures:

• Absolute: Delta(x) = |$x_i$ - $x_{mean}$| (same units as x)
• Relative: Delta$\frac{x}{x}$ (dimensionless)
• Percentage: $\frac{Delta(x}{x}$) * 100%

Propagation Rules:

1. Sum/Difference: absolute errors add
2. Product/Quotient: relative errors add
3. Power: relative error multiplied by power magnitude
4. General: Delta$\frac{A^p*B^q/C^r}{(A^p*B^q/C^r)}$ = |p|*Delta$\frac{A}{A}$ + |q|*Delta$\frac{B}{B}$ + |r|*Delta$\frac{C}{C}$

Critical insight: The variable with the highest power contributes the most error. In rho = $\frac{M}{pi*r^2*L}$, improving the measurement of r has the greatest impact on reducing the error in rho.

Subtraction trap: When A ≈ B, Delta$\frac{A-B}{(A-B)}$ can be enormous even if individual errors are small.