Convert ton / cubic foot to grain / cubic foot
Learn how to convert
1
ton / cubic foot to
grain / cubic foot
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{ton}{cubic \text{ } foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic \text{ } foot}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{ton}{cubic \text{ } foot}\right) = {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{cubic \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{2.8316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{ton}{cubic \text{ } foot}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{cubic \text{ } foot}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{2.8316846592}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{2.8316846592}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{5}}{2.8316846592}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{2.8316846592}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{5}}{2.8316846592} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-3}}{2.8316846592}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{10^{5}}{{\color{rgb(255,204,153)} \cancel{2.8316846592}}} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-3}}{{\color{rgb(255,204,153)} \cancel{2.8316846592}}}\)
\(\text{Simplify}\)
\(10^{5} = {\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-3} = 10^{5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{6.479891 \times 10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 6.479891 \times 10^{-3} \times \dfrac{1.0}{6.479891 \times 10^{-3}} = 10^{5} \times \dfrac{1.0}{6.479891 \times 10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = 10^{5} \times \dfrac{1.0}{6.479891 \times 10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{5}}{6.479891 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 10^{5}}{6.479891}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{8}}{6.479891}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx15432358.353\approx1.5432 \times 10^{7}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{ton}{cubic \text{ } foot}\right)\approx{\color{rgb(20,165,174)} 1.5432 \times 10^{7}}\left(\dfrac{grain}{cubic \text{ } foot}\right)\)
