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Part of JEXP-01 — Experimental Skills (JEE-specific 18 experiments)

Error Analysis and Significant Figures

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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: (Delta_x/x) x 100%. Error propagation for derived quantities: if Z = A^a * B^b / C^c, then Delta_Z/Z = a*(Delta_A/A) + b*(Delta_B/B) + c*(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 = FL/(pir^2Delta_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.

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