Convert grain / liter to pound / gallon

Learn how to convert 1 grain / liter to pound / gallon step by step.

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Calculation Breakdown

Set up the equation

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

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

\(\text{Left side: 1.0 } \left(\dfrac{grain}{liter}\right) = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{pound}{gallon}\right) = {\color{rgb(125,164,120)} \dfrac{0.45359237}{4.54609 \times 10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{0.45359237}{4.54609 \times 10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

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

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

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

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{0.45359237}{4.54609 \times 10^{-3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{0.45359237}{4.54609 \times 10^{-3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{0.45359237}{4.54609 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{6.479891 \times 10^{-5}}{10^{-3}} = {\color{rgb(20,165,174)} x} \times \dfrac{0.45359237}{4.54609 \times 10^{-3}}\)

Cancel factors on both sides

\(\text{Cancel factors}\)

\(\dfrac{6.479891 \times 10^{-5}}{{\color{rgb(255,204,153)} \cancel{10^{-3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{0.45359237}{4.54609 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}}\)

\(\text{Simplify}\)

\(6.479891 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times \dfrac{0.45359237}{4.54609}\)

Switch sides

\({\color{rgb(20,165,174)} x} \times \dfrac{0.45359237}{4.54609} = 6.479891 \times 10^{-5}\)

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

Multiply both sides by \(\left(\dfrac{4.54609}{0.45359237}\right)\)

\({\color{rgb(20,165,174)} x} \times \dfrac{0.45359237}{4.54609} \times \dfrac{4.54609}{0.45359237} = 6.479891 \times 10^{-5} \times \dfrac{4.54609}{0.45359237}\)

\(\text{Cancel}\)

\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{0.45359237}} \times {\color{rgb(99,194,222)} \cancel{4.54609}}}{{\color{rgb(99,194,222)} \cancel{4.54609}} \times {\color{rgb(255,204,153)} \cancel{0.45359237}}} = 6.479891 \times 10^{-5} \times \dfrac{4.54609}{0.45359237}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{6.479891 \times 10^{-5} \times 4.54609}{0.45359237}\)

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

\({\color{rgb(20,165,174)} x}\approx0.0006494414\approx6.4944 \times 10^{-4}\)

\(\text{Conversion Equation}\)

\(1.0\left(\dfrac{grain}{liter}\right)\approx{\color{rgb(20,165,174)} 6.4944 \times 10^{-4}}\left(\dfrac{pound}{gallon}\right)\)