Convert gram / cubic inch to grain / gallon

Learn how to convert 1 gram / cubic inch to grain / gallon step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{gram}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{gallon}\right)\)

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

\(\text{Left side: 1.0 } \left(\dfrac{gram}{cubic \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{grain}{gallon}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

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

\(1.0\left(\dfrac{gram}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{gallon}\right)\)

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

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-2}}{3.785411784}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{1.0}{1.6387064 \times 10^{-2}} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-2}}{3.785411784}\)

Switch sides

\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-2}}{3.785411784} = \dfrac{1.0}{1.6387064 \times 10^{-2}}\)

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

Multiply both sides by \(\left(\dfrac{3.785411784}{6.479891 \times 10^{-2}}\right)\)

\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-2}}{3.785411784} \times \dfrac{3.785411784}{6.479891 \times 10^{-2}} = \dfrac{1.0}{1.6387064 \times 10^{-2}} \times \dfrac{3.785411784}{6.479891 \times 10^{-2}}\)

\(\text{Cancel}\)

\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{3.785411784}}}{{\color{rgb(166,218,227)} \cancel{3.785411784}} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = \dfrac{1.0 \times 3.785411784}{1.6387064 \times 10^{-2} \times 6.479891 \times 10^{-2}}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{3.785411784}{1.6387064 \times 10^{-2} \times 6.479891 \times 10^{-2}}\)

Rewrite equation

\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 10^{2} \times 3.785411784}{1.6387064 \times 6.479891}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{4} \times 3.785411784}{1.6387064 \times 6.479891}\)

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

\({\color{rgb(20,165,174)} x}\approx3564.8747795\approx3.5649 \times 10^{3}\)

\(\text{Conversion Equation}\)

\(1.0\left(\dfrac{gram}{cubic \text{ } inch}\right)\approx{\color{rgb(20,165,174)} 3.5649 \times 10^{3}}\left(\dfrac{grain}{gallon}\right)\)