Convert grain / gallon to pound / gallon
Learn how to convert
1
grain / gallon to
pound / gallon
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{gallon}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{gallon}\right) = {\color{rgb(125,164,120)} \dfrac{453.59237}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{453.59237}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{gallon}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{453.59237}{3.785411784}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{453.59237}{3.785411784}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{453.59237}{3.785411784}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{6.479891 \times 10^{-2}}{3.785411784} = {\color{rgb(20,165,174)} x} \times \dfrac{453.59237}{3.785411784}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{6.479891 \times 10^{-2}}{{\color{rgb(255,204,153)} \cancel{3.785411784}}} = {\color{rgb(20,165,174)} x} \times \dfrac{453.59237}{{\color{rgb(255,204,153)} \cancel{3.785411784}}}\)
\(\text{Simplify}\)
\(6.479891 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times 453.59237\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 453.59237 = 6.479891 \times 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{453.59237}\right)\)
\({\color{rgb(20,165,174)} x} \times 453.59237 \times \dfrac{1.0}{453.59237} = 6.479891 \times 10^{-2} \times \dfrac{1.0}{453.59237}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{453.59237}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{453.59237}}} = 6.479891 \times 10^{-2} \times \dfrac{1.0}{453.59237}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.479891 \times 10^{-2}}{453.59237}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0001428571\approx1.4286 \times 10^{-4}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{gallon}\right)\approx{\color{rgb(20,165,174)} 1.4286 \times 10^{-4}}\left(\dfrac{pound}{gallon}\right)\)
