Convert grain / gallon to grain / cubic meter
Learn how to convert
1
grain / gallon to
grain / cubic meter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic \text{ } meter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{4.40488377086 \times 10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{4.40488377086 \times 10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{cubic \text{ } meter}\right) = {\color{rgb(125,164,120)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic \text{ } meter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{4.40488377086 \times 10^{-3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 6.479891 \times 10^{-5}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{4.40488377086 \times 10^{-3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{4.40488377086 \times 10^{-3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 6.479891 \times 10^{-5}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{6.479891 \times 10^{-5}}{4.40488377086 \times 10^{-3}} = {\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-5}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}}}{4.40488377086 \times 10^{-3}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{4.40488377086 \times 10^{-3}} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{4.40488377086 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3}}{4.40488377086}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx227.02074607\approx2.2702 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{gallon}\right)\approx{\color{rgb(20,165,174)} 2.2702 \times 10^{2}}\left(\dfrac{grain}{cubic \text{ } meter}\right)\)
