Question

How do we convert \[{\text{ 1 }}g/c{m^3}{\text{ to }}kg/{m^3}?\]

Answer 1

Hint: In order to solve this question, we need to understand that we need to convert the given units in S.I. unit, we have to convert it in \[kg/{m^3}\], so we will use some basic conversion as 1 kg=1000 g and 1 m=100 cm, by using it we will get the required answer.

Complete step by step solution:
Dimensions of Density are \[M{\text{ }}{L^{ - 3}}\]
We know that,
1 kg=1000 g
1 m= 100 cm
So simultaneously we have:
\[{\text{1 g = }}\dfrac{1}{{1000}}{\text{ kg }} \Rightarrow {\text{1}}{{\text{0}}^{ - 3}}{\text{ }}kg\]
\[{\text{1 cm = }}\dfrac{1}{{100}}{\text{ m}} \Rightarrow {10^{ - 2}}{\text{ m}}\]
Let us convert it to a standard unit \[kg/{m^3}\] by the use of conversion terms shown above.
\[ \Rightarrow {\text{ 1 }}\dfrac{g}{{c{m^3}}}{\text{ }}\]
\[ \Rightarrow {\text{1}} \times \dfrac{{1{\text{ }}g}}{{1{\text{ }}c{m^3}}}\]
\[ \Rightarrow {\text{1}} \times \dfrac{{1{\text{ }}g}}{{{{\left( {1{\text{ }}cm} \right)}^3}}}\]
Conversion takes place,
\[ \Rightarrow {\text{1}} \times \dfrac{{{{10}^{ - 3}}{\text{ k}}g}}{{{{\left( {{{10}^{ - 2}}{\text{ }}m} \right)}^3}}}\]
Solving the denominator term,
\[ \Rightarrow {\text{1}} \times \dfrac{{{{10}^{ - 3}}{\text{ k}}g}}{{{{10}^{ - 6}}{\text{ }}{{\text{m}}^3}}}\]
Solving numerator and denominator we get,
\[ \Rightarrow {\text{1}} \times \dfrac{{{{10}^3}{\text{ k}}g}}{{{{\text{m}}^3}}}\]
\[ \Rightarrow {10^3} \times \dfrac{{{\text{ k}}g}}{{{{\text{m}}^3}}}\]
\[ \therefore {10^3}{\text{ kg/}}{{\text{m}}^3}\]

Note:
It should be remembered that Conversion of units is the measure of transforming the particular measurement of any specific physical quantity into one form of units. A g is a short form of grams and kg is a short form of a kilogram. A gram and a kilogram are a unit of mass in the international system of units. Students must follow the basic steps. There are formulas for direct conversion from one unit to another which can be used as well.