physics_units_measurements
 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$𝛥{a}_{mean}=\frac{|𝛥{a}_{1}|+|𝛥{a}_{2}|+|𝛥{a}_{3}|+\phantom{\rule{0.22em}{0ex}}.\phantom{\rule{0.22em}{0ex}}.\phantom{\rule{0.22em}{0ex}}.\phantom{\rule{0.22em}{0ex}}+|𝛥{a}_{n}|\phantom{\rule{0.22em}{0ex}}}{n}$ Relative ErrorThe relative error is the ratio of the mean absolute error 𝛥amean$𝛥{a}_{mean}$ to the meanvalue amean${a}_{mean}$ of the quantity measured.Relative Error=𝛥ameanamean$Relative\phantom{\rule{0.22em}{0ex}}Error=\frac{𝛥{a}_{mean}}{{a}_{mean}}$ Percentage ErrorPercentage Error=𝛥ameanamean×100 %$Percentage\phantom{\rule{0.22em}{0ex}}Error=\frac{𝛥{a}_{mean}}{{a}_{mean}}×100\phantom{\rule{0.22em}{0ex}}%$ 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
 Questions Q-1. A cube has sides of 1.2×10-2m$1.2×{10}^{-2}m$. Calculate its volume A-1V=(1.2×10-2)3 m3$V=\left(1.2×{10}^{-2}{\right)}^{3}\phantom{\rule{0.22em}{0ex}}{m}^{3}$⟹V=1.728×10-6 m3$V=1.728×{10}^{-6}\phantom{\rule{0.22em}{0ex}}{m}^{3}$ as there are 2 significant numbers in side so⟹V=1.7×10-6 m3$V=1.7×{10}^{-6}\phantom{\rule{0.22em}{0ex}}{m}^{3}$