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(x)/x (dimensionless)
• Percentage: (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(A^pB^q/C^r)/(A^pB^q/C^r) = |p|*Delta(A)/A + |q|*Delta(B)/B + |r|*Delta(C)/C

Critical insight: The variable with the highest power contributes the most error. In rho = M/(pir^2L), improving the measurement of r has the greatest impact on reducing the error in rho.

Subtraction trap: When A ≈ B, Delta(A-B)/(A-B) can be enormous even if individual errors are small.