Convert grain / gallon to grain / cubic yard
Learn how to convert
1
grain / gallon to
grain / cubic yard
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic \text{ } yard}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{6.479891}{454.609}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{6.479891}{454.609}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{cubic \text{ } yard}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic \text{ } yard}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891}{454.609}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{6.479891}{454.609}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891}{454.609}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.764554857984}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{6.479891}{454.609} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.764554857984}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}}}{454.609} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times 10^{-5}}{0.764554857984}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{454.609} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-5}}{0.764554857984}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-5}}{0.764554857984} = \dfrac{1.0}{454.609}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{0.764554857984}{10^{-5}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-5}}{0.764554857984} \times \dfrac{0.764554857984}{10^{-5}} = \dfrac{1.0}{454.609} \times \dfrac{0.764554857984}{10^{-5}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-5}}} \times {\color{rgb(99,194,222)} \cancel{0.764554857984}}}{{\color{rgb(99,194,222)} \cancel{0.764554857984}} \times {\color{rgb(255,204,153)} \cancel{10^{-5}}}} = \dfrac{1.0 \times 0.764554857984}{454.609 \times 10^{-5}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.764554857984}{454.609 \times 10^{-5}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-5}}\text{ can be rewritten to }10^{5}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 0.764554857984}{454.609}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx168.17855739\approx1.6818 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{gallon}\right)\approx{\color{rgb(20,165,174)} 1.6818 \times 10^{2}}\left(\dfrac{grain}{cubic \text{ } yard}\right)\)
