Convert grain / cubic yard to pound / cubic meter
Learn how to convert
1
grain / cubic yard to
pound / cubic meter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{cubic \text{ } yard}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } meter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{cubic \text{ } yard}\right) = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } meter}\right) = {\color{rgb(125,164,120)} 0.5\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 0.5\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } yard}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } meter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 0.5}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 0.5} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 0.5} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{6.479891 \times 10^{-5}}{0.764554857984} = {\color{rgb(20,165,174)} x} \times 0.5\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 0.5 = \dfrac{6.479891 \times 10^{-5}}{0.764554857984}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{0.5}\right)\)
\({\color{rgb(20,165,174)} x} \times 0.5 \times \dfrac{1.0}{0.5} = \dfrac{6.479891 \times 10^{-5}}{0.764554857984} \times \dfrac{1.0}{0.5}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{0.5}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{0.5}}} = \dfrac{6.479891 \times 10^{-5} \times 1.0}{0.764554857984 \times 0.5}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.479891 \times 10^{-5}}{0.764554857984 \times 0.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0001695075\approx1.6951 \times 10^{-4}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } yard}\right)\approx{\color{rgb(20,165,174)} 1.6951 \times 10^{-4}}\left(\dfrac{pound}{cubic \text{ } meter}\right)\)
