• $summary_{type}$: revision
• $word_{count}$: 170

Errors are systematic (consistent bias — calibration, zero error) or random (statistical fluctuation). Systematic errors affect accuracy; random errors affect precision. Absolute error: $Delta_x$ = |$x_{measured}$ - $x_{true}$|. Relative error: $Delta_x$/x. Percentage error: $\frac{Delta_x}{x}$ x 100%. Error propagation for derived quantities: if Z = $A^a$ * $B^b$ / $C^c$, then $Delta_Z$/Z = a*$\frac{Delta_A}{A}$ + b*$\frac{Delta_B}{B}$ + c*$\frac{Delta_C}{C}$. For addition/subtraction: absolute errors add. For multiplication/division: relative errors add. The variable with the highest power contributes most to error. Example: in Y = $\frac{FL}{pi*r^2*Delta_L}$, the percentage error in r is doubled (power 2). Significant figures: the result should have the same number of significant figures as the least precise measurement. Least count determines the precision of direct measurements. Graphical analysis: plot the relevant graph ($T^2$ vs L, stress vs strain, etc.) and use the slope/intercept to determine the physical quantity. The graph automatically averages out random errors.