Units and Measurements
Systematic errors: It tends to be in one direction, either positive or negative.a. Instrumental errors b. Imperfection in experimental technique or procedure.c. Personal errors
Random Errors
Least count error
Absolute ErrorThe magnitude of the difference between the true value of the quantityand the individual measurement value is called the absolute error of themeasurement.
The arithmetic mean of all the absolute errors is taken as the final or mean absolute errorof the value of the physical quantity a. 𝛥amean=|𝛥a1|+|𝛥a2|+|𝛥a3|+...+|𝛥an|n
Relative ErrorThe relative error is the ratio of the mean absolute error 𝛥amean to the meanvalue amean of the quantity measured.RelativeError=𝛥ameanamean
Percentage ErrorPercentageError=𝛥ameanamean×100%
Rules for Arithmetic Operations with Significant Figures(1) In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures. (2) In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.
Rounding off the Uncertain Digits
Q-1. A cube has sides of 1.2×10-2m. Calculate its volume A-1V=(1.2×10-2)3m3V=1.728×10-6m3 as there are 2 significant numbers in side soV=1.7×10-6m3