Question

Which of the following fractions can be used in the conversion of 27 cm3 to the unit m3?
1M/10^-2Cm
1ML/1Cm^3
(10^2M/1M)^3
(1M/10^2Cm)^3

Answer 1

\[1[\text m]=100[\text{cm}]=10^2[\text{cm}]\]
\[1[\text m]^3=(100[\text{cm}])^3=\big(10^2[\text{cm}]\big)^3=10^6[\text{cm}]^3\]
\[\frac{1[\text m]^3}{10^6[\text{cm}]^3}=1\]

\[27 [\text{cm}]^3\\=27 [\text{cm}]^3\times1\\
=27 [\text{cm}]^3\times\frac{1[\text m]^3}{10^6[\text{cm}]^3}\\
=\frac{27}{10^6}[\text m]^3\]