Convert grain / cubic meter to pound / cubic foot
Learn how to convert
1
grain / cubic meter to
pound / cubic foot
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{45.359237}{2.8316846592}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(6.479891 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times \dfrac{45.359237}{2.8316846592}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{45.359237}{2.8316846592} = 6.479891 \times 10^{-5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{2.8316846592}{45.359237}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{45.359237}{2.8316846592} \times \dfrac{2.8316846592}{45.359237} = 6.479891 \times 10^{-5} \times \dfrac{2.8316846592}{45.359237}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{45.359237}} \times {\color{rgb(99,194,222)} \cancel{2.8316846592}}}{{\color{rgb(99,194,222)} \cancel{2.8316846592}} \times {\color{rgb(255,204,153)} \cancel{45.359237}}} = 6.479891 \times 10^{-5} \times \dfrac{2.8316846592}{45.359237}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.479891 \times 10^{-5} \times 2.8316846592}{45.359237}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000040453\approx4.0453 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 4.0453 \times 10^{-6}}\left(\dfrac{pound}{cubic \text{ } foot}\right)\)
