Convert pound / cubic meter to grain / barrel
Learn how to convert
1
pound / cubic meter to
grain / barrel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{barrel}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 0.5\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 0.5\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{barrel}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.119240471196}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.119240471196}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{barrel}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 0.5} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.119240471196}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 0.5} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.119240471196}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 0.5} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.119240471196}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(0.5 = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.119240471196}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.119240471196} = 0.5\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{0.119240471196}{6.479891 \times 10^{-5}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.119240471196} \times \dfrac{0.119240471196}{6.479891 \times 10^{-5}} = 0.5 \times \dfrac{0.119240471196}{6.479891 \times 10^{-5}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}} \times {\color{rgb(166,218,227)} \cancel{0.119240471196}}}{{\color{rgb(166,218,227)} \cancel{0.119240471196}} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}}} = 0.5 \times \dfrac{0.119240471196}{6.479891 \times 10^{-5}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.5 \times 0.119240471196}{6.479891 \times 10^{-5}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-5}}\text{ can be rewritten to }10^{5}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 0.5 \times 0.119240471196}{6.479891}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx920.08084084\approx9.2008 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 9.2008 \times 10^{2}}\left(\dfrac{grain}{barrel}\right)\)
