Question

Ask (a) what is the area and uncertainty in area of one side of a rectangular wooden board that has a length of (21.2 ± 0.3) cm and a width of (9.8 ± 0.1) cm? (Give your answers in cm2.) (g17 2 1-10-2 Your answer cannot be understood or graded. More Information ± x cm2 0.4 (b) what if? If the thickness of the board is (1.1 ±。2) cm, what is the volume of the board and the uncertainty in this volume? (Give your answers in cms.) cm Need Help? Read it

This is about using proper number of significant figures

Answer 1

Length = (21.2 plusminus 0.3)cm width = (9.8 plusminus 0.1)cm Now, Area = A = l times b therefore A = 21.2 times 9.8 = 207.76 Since the least number of significant digit is 2 therefore Area = A = 2.10 times 10^2 = 2.1 times 10^2 cm^2 Now for uncertainty, we know that relative errors are added during multiplication. therefore relative error in A = delta A/A delta A/A = delta l/l + delta w/w [where l and w are length and width] therefore delta A/A = 0.3/21.2 + 0.1/9.8 delta A/A = 0.01415 + 0.0102 Now correcting to correct deprival places delta A/A = 0.01 + 0.01 = 0.02 therefore delta A = 0.02 times A = 0.02 times 2.1 times 10^2 cm^2 \r\n delta A = 0.042 times 10^2 = 0.04 times 10^2 delta A = 4 cm^2 therefore area = (2.1 times 10^2 plusminus 4)cm^2 thickness = t = (1.1 plusminus 0.2)cm Now, volume = V