Convert pound / cubic meter to kilogram / cubic meter
Learn how to convert
1
pound / cubic meter to
kilogram / cubic meter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 0.45359237\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 0.45359237\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{cubic \text{ } meter}\right) = {\color{rgb(125,164,120)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Define the values of the selected prefixes
\(\text{Right side: } \dfrac{kilo}{1.0} = \dfrac{k}{1.0} = {\color{rgb(204,139,6)} \dfrac{10^{3}}{1.0}}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 0.45359237} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(204,139,6)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(125,164,120)} 10^{-3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 0.45359237} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(204,139,6)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(125,164,120)} 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 0.45359237} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(204,139,6)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(125,164,120)} 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(0.45359237 = {\color{rgb(20,165,174)} x} \times 10^{-3} \times \dfrac{10^{3}}{1.0}\)
\(\text{Simplify}\)
\(0.45359237 = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = 0.45359237\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 0.45359237\approx4.5359 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 4.5359 \times 10^{-1}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
