Convert pound / barrel to grain / cubic

Learn how to convert 1 pound / barrel to grain / cubic step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{pound}{barrel}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic}\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)

\(\text{Left side: 1.0 } \left(\dfrac{pound}{barrel}\right) = {\color{rgb(89,182,91)} \dfrac{5.0}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{5.0}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{grain}{cubic}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{4168181825.44058}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{4168181825.44058}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(\dfrac{pound}{barrel}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic}\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{5.0}{1.19240471196}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{4168181825.44058}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{5.0}{1.19240471196}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{4168181825.44058}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{5.0}{1.19240471196}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{4168181825.44058}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{5.0}{1.19240471196} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{4168181825.44058}\)

Switch sides

\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{4168181825.44058} = \dfrac{5.0}{1.19240471196}\)

Isolate \({\color{rgb(20,165,174)} x}\)

Multiply both sides by \(\left(\dfrac{4168181825.44058}{6.479891 \times 10^{-5}}\right)\)

\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{4168181825.44058} \times \dfrac{4168181825.44058}{6.479891 \times 10^{-5}} = \dfrac{5.0}{1.19240471196} \times \dfrac{4168181825.44058}{6.479891 \times 10^{-5}}\)

\(\text{Cancel}\)

\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}} \times {\color{rgb(166,218,227)} \cancel{4168181825.44058}}}{{\color{rgb(166,218,227)} \cancel{4168181825.44058}} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}}} = \dfrac{5.0 \times 4168181825.44058}{1.19240471196 \times 6.479891 \times 10^{-5}}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{5.0 \times 4168181825.44058}{1.19240471196 \times 6.479891 \times 10^{-5}}\)

Rewrite equation

\(\dfrac{1.0}{10^{-5}}\text{ can be rewritten to }10^{5}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 5.0 \times 4168181825.44058}{1.19240471196 \times 6.479891}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx2.6972753028 \times 10^{14}\approx2.6973 \times 10^{14}\)

\(\text{Conversion Equation}\)

\(1.0\left(\dfrac{pound}{barrel}\right)\approx{\color{rgb(20,165,174)} 2.6973 \times 10^{14}}\left(\dfrac{grain}{cubic}\right)\)