If the density of methane gas is 0.66kg/m3, then what is the density of methane in cm3?

If the density of methane gas is 0.66kg/m3, then what is the density of methane in cm3 ?

$$0.66\ \dfrac{ \rm{kg} } { \rm{m^3} } \\\\
=0.66\ \dfrac{ \rm{kg} } { \rm{m}\cdot\rm{m}\cdot\rm{m} } \\\\
=0.66\ \dfrac{ \rm{kg} } { \rm{m}\cdot\rm{m}\cdot\rm{m} }
\cdot \dfrac{ 1\ \rm{m} }{ 100\ \rm{cm }}
\cdot \dfrac{ 1\ \rm{m} }{ 100\ \rm{cm }}
\cdot \dfrac{ 1\ \rm{m} }{ 100\ \rm{cm }}\\\\
=0.66\ \dfrac{ \rm{kg} } { \rm{\not{m}}\cdot\rm{\not{m}}\cdot\rm{\not{m}} }
\cdot \dfrac{ 1\ \rm{\not{m}} }{ 100\ \rm{cm}}
\cdot \dfrac{ 1\ \rm{\not{m}} }{ 100\ \rm{cm}}
\cdot \dfrac{ 1\ \rm{\not{m}} }{ 100\ \rm{cm}}\\\\
=0.66\ \dfrac{ \rm{kg} } { 100\ \rm{cm } \cdot 100\ \rm{cm} \cdot 100\ \rm{cm} } \\\\
=0.66\ \dfrac{ \rm{kg} } { 100\cdot 100\cdot 100\cdot \rm{cm}\cdot \rm{cm}\cdot \rm{cm}} \\\\
=0.66\ \dfrac{ \rm{kg} } { 100\cdot 100\cdot 100\cdot \rm{cm^3}} \\\\
=\dfrac{0.66\ }{100\cdot 100\cdot 100}\cdot \dfrac{ \rm{kg} } { \rm{cm^3}} \\\\
=\dfrac{0.66\ }{10^2\cdot 10^2\cdot 10^2}\cdot \dfrac{ \rm{kg} } { \rm{cm^3}} \\\\
=\dfrac{0.66\ }{ 10^6 } \cdot \dfrac{ \rm{kg} } { \rm{cm^3}} \\\\
=0.66\cdot 10^{-6} \cdot \dfrac{ \rm{kg} } { \rm{cm^3}}$$

$$\\=6.6 \cdot 10^{-1} \cdot 10^{-6} \cdot \dfrac{ \rm{kg} } { \rm{cm^3} }\\\\
=6.6 \cdot 10^{-7}\cdot \dfrac{ \rm{kg} } { \rm{cm^3} }\\\\$$

Presumably you mean what is the density in gm/cm³

0.66kg/m³ = 0.66*1000gm/(100cm)³  = 0.00066 gm/cm³

.

To convert from $${\frac{{\mathtt{1}}}{{{\mathtt{m}}}^{{\mathtt{3}}}}}$$ to $${\frac{{\mathtt{1}}}{{{\mathtt{cm}}}^{{\mathtt{3}}}}}$$ you calculate $${\frac{{\mathtt{1}}}{{{\mathtt{m}}}^{{\mathtt{3}}}}} = {\frac{{{\mathtt{m}}}^{{\mathtt{3}}}}{\left({\mathtt{100}}{cm}{\mathtt{\,\times\,}}{\mathtt{100}}{cm}{\mathtt{\,\times\,}}{\mathtt{100}}{cm}\right)}} = {\frac{{{\mathtt{m}}}^{{\mathtt{3}}}}{\left({\mathtt{1\,000\,000}}\left[{{cm}}^{{\mathtt{3}}}\right]\right)}}$$.

So to solve your equation you devide by $${\mathtt{1\,000\,000}}\left[{{cm}}^{{\mathtt{3}}}\right]$$.

$${\frac{{\mathtt{0.66}}{kg}}{\left({{\mathtt{m}}}^{{\mathtt{3}}}\right)}}{\mathtt{\,\times\,}}\left({\frac{{{\mathtt{m}}}^{{\mathtt{3}}}}{{\mathtt{1\,000\,000}}\left[{{cm}}^{{\mathtt{3}}}\right]}}\right) = {\frac{{\mathtt{0.66}}{kg}}{\left({\mathtt{1\,000\,000}}\left[{{cm}}^{{\mathtt{3}}}\right]\right)}} = {\mathtt{6.6}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{7}}\right)}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{kg}}}{\left({{\mathtt{cm}}}^{{\mathtt{3}}}\right)}}\right)$$

The result is $${\mathtt{6.6}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{7}}\right)}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{kg}}}{{{\mathtt{cm}}}^{{\mathtt{3}}}}}\right)$$