(Solved): A student determines the area of a rectangle by measuring the lengths of its sides, using a ruler s ...

A student determines the area of a rectangle by measuring the lengths of its sides, using a ruler scribed in centimeters with subdivisions in millimeters. Assume that measurements made with the ruler are accurate to within + or $?1\mathrm{mm}$. The values that the student records are length $=16.9\mathrm{cm}$ and width $=14.8\mathrm{cm}$. 1. To 2 decimal places, the calculated value of the area (length $\times$ width) is $250.12{\mathrm{cm}}^2$. Based on the significant figure rule for multiplication, how should the area be reported? Area $=?{\mathrm{cm}}^2$ 2. Including the uncertainty in the measurements, (a) how should the length be reported? $16.9\mathrm{cm}+$ or - $\mathrm{cm}$ (b) how should the width be reported? $14.8\mathrm{cm}+$ or - $\mathrm{cm}$ 3. Use the values from 2. and common sense here. (a) To 2 decimal places, what is the maximum calculated value for the area? ${\mathrm{cm}}^2$ (b) To 2 decimal places, what is the minimum calculated value for the area? ${\mathrm{cm}}^2$ (c) Including the uncertainty, how should the area calculated from the recorded length and width be reported? Hint: Use the range from (a) and (b) to determine the + or - uncertainty in the area to 1 sig fig and do not report the area beyond the first digit containing the uncertainty. Area $=$ ${\mathrm{cm}}^2+$ or - ${\mathrm{cm}}^2$ 4. Do the methods of reporting the area in 1 and 3 give the same number of significant figures? 6 more group attempts remaining (a) Atoms are very small compared to objects on the macroscopic scale. The radius of a chromium atom is $126\mathrm{pm}$. What is this value in meters and in centimeters? $\mathrm{m}$ $\mathrm{cm}$ (b) The mass of a single chromium atom is $8.63\times 10^{?23}\mathrm{g}$. Suppose enough $\mathrm{Cr}$ atoms were lined up like beads on a string to span a distance of $34.7\mathrm{cm}$ ( 14 inches). How many atoms would be required? atoms What mass in grams of $\mathbf{Cr}$ would be used? g Could you weigh out this amount of chromium using a typical laboratory balance? (c) Taking the density of chromium metal to be $7.00\mathrm{g}/{\mathrm{cm}}^3$, calculate the mass of metal needed to form a piece of $\mathbf{Cr}$ wire with the same length as the distance in $b$, but with a diameter of $1.00\mathrm{mm}$. Hint: The volume of a cylinder is $?$ times its radius squared times its height. $\left(V=?r^{2}h\right)$ $\mathrm{g}$ How many chromium atoms does this represent? atoms 4 more group attempts remaining