Convert pound / gallon to grain / liter
Learn how to convert
1
pound / gallon to
grain / liter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{liter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{453.59237}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{453.59237}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{liter}\right) = {\color{rgb(125,164,120)} 6.479891 \times 10^{-2}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 6.479891 \times 10^{-2}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{liter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{453.59237}{3.785411784}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 6.479891 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{453.59237}{3.785411784}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 6.479891 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{453.59237}{3.785411784}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 6.479891 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{453.59237}{3.785411784} = {\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-2} = \dfrac{453.59237}{3.785411784}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{6.479891 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-2} \times \dfrac{1.0}{6.479891 \times 10^{-2}} = \dfrac{453.59237}{3.785411784} \times \dfrac{1.0}{6.479891 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = \dfrac{453.59237 \times 1.0}{3.785411784 \times 6.479891 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{453.59237}{3.785411784 \times 6.479891 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 453.59237}{3.785411784 \times 6.479891}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1849.2043665\approx1.8492 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{gallon}\right)\approx{\color{rgb(20,165,174)} 1.8492 \times 10^{3}}\left(\dfrac{grain}{liter}\right)\)
