Problem 48
Express the answers to the following calculations in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)
Problem 49
Express the answers to the following calculations in scientific notation: (a) \(0.0095+\left(8.5 \times 10^{-3}\right)\) (b) \(653 \div\left(5.75 \times 10^{-8}\right)\) (c) \(850,000-\left(9.0 \times 10^{5}\right)\) (d) \(\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^{6}\right)\)
Problem 50
Determine the number of significant figures in each of the following measurements: (a) \(4867 \mathrm{mi}\), (b) \(56 \mathrm{~mL}\) (c) 60,104 tons, (d) \(2900 \mathrm{~g}\), (e) \(40.2 \mathrm{~g} / \mathrm{cm}^{3}\) (f) \(0.0000003 \mathrm{~cm},(\mathrm{~g}) 0.7 \mathrm{~min}\) (h) \(4.6 \times 10^{19}\) atoms.
Problem 51
Determine the number of significant figures in each of the following measurements: (a) \(0.006 \mathrm{~L},\) (b) \(0.0605 \mathrm{dm}\) (c) \(60.5 \mathrm{mg}\), (d) \(605.5 \mathrm{~cm}^{2}\) (e) \(9.60 \times 10^{3} \mathrm{~g}\) (f) \(6 \mathrm{~kg}\), (g) \(60 \mathrm{~m}\).
Problem 52
Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) \(5.6792 \mathrm{~m}+0.6 \mathrm{~m}+4.33 \mathrm{~m}\) (b) \(3.70 \mathrm{~g}-2.9133 \mathrm{~g}\) (c) \(4.51 \mathrm{~cm} \times 3.6666 \mathrm{~cm}\)
Problem 53
Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) \(7.310 \mathrm{~km} \div 5.70 \mathrm{~km}\) (b) \(\left(3.26 \times 10^{-3} \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \mathrm{mg}\right)\) (c) \(\left(4.02 \times 10^{6} \mathrm{dm}\right)+\left(7.74 \times 10^{7} \mathrm{dm}\right)\)
Problem 54
Three students \((\mathrm{A}, \mathrm{B},\) and \(\mathrm{C})\) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are: \(\mathrm{A}(87.1,88.2,87.6) ; \mathrm{B}(86.9,\) 87.1,87.2 ; \(\mathrm{C}(87.6,87.8,87.9)\). The true volume is \(87.0 \mathrm{~mL}\). Comment on the precision and the accuracy of each student's results.
Problem 55
Three apprentice tailors \((\mathrm{X}, \mathrm{Y},\) and \(\mathrm{Z})\) are assigned the task of measuring the seam of a pair of trousers. Each one makes three measurements. The results in inches are \(\mathrm{X}(31.5,31.6,31.4) ; \mathrm{Y}(32.8,32.3,32.7) ; \mathrm{Z}(31.9,\) 32.2,32.1 ). The true length is 32.0 in. Comment on the precision and the accuracy of each tailor's measurements.
Problem 56
Carry out the following conversions: (a) \(22.6 \mathrm{~m}\) to decimeters, (b) \(25.4 \mathrm{mg}\) to kilograms, (c) \(556 \mathrm{~mL}\) to liters, (d) \(10.6 \mathrm{~kg} / \mathrm{m}^{3}\) to \(\mathrm{g} / \mathrm{cm}^{3}\).
Problem 57
Carry out the following conversions: (a) \(22.6 \mathrm{~m}\) to decimeters, (b) \(25.4 \mathrm{mg}\) to kilograms, (c) \(556 \mathrm{~mL}\) to liters, (d) \(10.6 \mathrm{~kg} / \mathrm{m}^{3}\) to \(\mathrm{g} / \mathrm{cm}^{3}\).
