Significant Figures

The mass of a box measured by a grocer’s balance is $2.30 \mathrm{kg}$. Two gold pieces of masses $20.15 \mathrm{g}$ and $20.17 \mathrm{g}$ are added to the box. What is the difference in the masses of the pieces to correct significant figures?

State the number of significant figures in the following:

$0.0006032 {\mathrm{m}}^2$

State the number of significant figures in the following:

$6.032 \mathrm{N} {\mathrm{m}}^{-2}$

State the number of significant figures in the following :

$6.320 \mathrm{J}$

State the number of significant figures in the following:

$0.2370 \mathrm{g} {\mathrm{cm}}^{-3}$

State the number of significant figures in the following:

$2.64\times {10}^{24} \mathrm{kg}$

State the number of significant figures in the following quantity:

$0.007 {\mathrm{m}}^2$

The unit of length convenient on the nuclear scale is a fermi: $1 \mathrm{f}={10}^{-15} \mathrm{m}$. Nuclear sizes obey roughly the following empirical relation: $r=r_0\mathit{ }{A}^{1/3}$ where $r$ is the radius of the nucleus, $A$ its mass number, and $r_0$ is a constant equal to $1.2 \mathrm{f}$. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom i.e $0.58\times {10}^3 {\mathrm{kgm}}^{-3}$.

Estimate the average mass density of a sodium atom assuming its size to be about $2.5 \mathrm{\AA }$. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: $970 {\mathrm{kgm}}^{-3}$. Are the two densities of the same order of magnitude? If so, why?

The Sun is a hot plasma (ionised matter) with its inner core at a temperature exceeding ${10}^7 \mathrm{K}$, and its outer surface at a temperature of about $6000 \mathrm{K}$. At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases?  Check if your guess is correct from the following data: mass of the Sun$=2.0\times {10}^{30} \mathrm{kg}$, radius of the Sun$=7.0\times {10}^8 \mathrm{m}$. 

One mole of an ideal gas at standard temperature and pressure occupies $22.4 \mathrm{L}$ (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen? (Consider the size of hydrogen molecule to be about $1 \mathrm{\AA }$). Why is this ratio so large? 

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\mathrm{\AA }$: $1 \mathrm{\AA }={10}^{-10} \mathrm{m}$. The size of a hydrogen atom is about $0.5 \mathrm{\AA }$. What is the total atomic volume in ${\mathrm{m}}^3$ of a mole of hydrogen atoms?

The mass of a box measured by a grocer’s balance is $2.3 \mathrm{kg}$. Two gold pieces of masses $20.15 \mathrm{g}$ and $20.17 \mathrm{g}$ are added to the box. What is the total mass (in $\mathrm{kg}$) of the box to correct significant figures?

The length, breadth and thickness of a rectangular sheet of metal are $4.234 \mathrm{m}$, $1.005 \mathrm{m}$, and $2.01 \mathrm{cm}$ respectively. Give the area and volume of the sheet to correct significant figures.