Question

The density of Aluminium is 3.7$g/c{m^3}$. Express it in $kg/{m^3}$.

Answer 1

Hint: One kilogram is equal to one thousand grams and one metre is equal to the hundred centimetres. Using this information and inserting it into the left hand side, we shall be able to convert the units and obtain the required answer.

Complete answer:
As we know that one kilogram is equal to one thousand grams. Therefore, we have
$1kg = 1000g$
Since we need to convert grams into kilograms, we can write the above value in terms of grams in the following way.
$1g = {10^{ - 3}}kg$
Also, one metre is equal to the hundred centimetres. Therefore, we have
$1m = 100cm$
Since we need to convert centimetres into metres, we can write the above value in terms of centimetres in the following way.
$1cm = {10^{ - 2}}m$
Now we can insert these values into the left hand side of the given expression. Doing so we get
$1g/c{m^3} = \dfrac{{1g}}{{1c{m^3}}} = \dfrac{{{{10}^{ - 3}}kg}}{{{{\left( {{{10}^{ - 2}}} \right)}^3}{m^3}}} = {10^{ - 3 + 6}}kg/{m^3} = {10^3}kg/{m^3}$
Now we can convert the given value into required units in the following way.
$3.7g/c{m^3} = 3.7 \times {10^3}kg/{m^3} = 3700kg/{m^3}$
This is the required answer.

Additional information:
The unit of a quantity refers to an internationally accepted standard unit used for measuring that quantity. The units are defined for the physical quantities to have a fixed standard for the measurement of different quantities. The most commonly used system is the S.I. system of units. Other systems of units are the C.G.S. system, M.K.S. system, etc.
The S.I. unit of mass is kilograms ($kg$). It is a fundamental quantity. Velocity is derived from the fundamental quantities, length and time and has S.I. units of metre per second ($m{s^{ - 1}}$).
The S.I. unit of momentum is equal to the product of S.I. units of mass and velocity, that is, kilogram metre per second ($kgm{s^{ - 1}}$)
The student shows that while solving problems all the units of various quantities must be in the same system of units.

Note:
It should be noted that in this question, we are converting C.G.S. units into S.I. units. The kilogram and metres are the SI units of mass and length respectively while the grams and the centimetres are the C.G.S. units of mass and length respectively.