# Convert kilogram / cubic meter to grain / barrel

Learn how to convert 1 kilogram / cubic meter to grain / barrel step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{barrel}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{gram}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{grain}{barrel}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.16365924}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.16365924}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
Define the values of the selected prefixes
$$\text{Left side: } \dfrac{kilo}{1.0} = \dfrac{k}{1.0} = {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{barrel}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.16365924}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.16365924}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{0.16365924}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}$$
$$\text{Conversion Equation}$$
$$10^{-3} \times \dfrac{10^{3}}{1.0} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.16365924}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.16365924}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.16365924} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{0.16365924}{6.479891 \times 10^{-5}}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{0.16365924} \times \dfrac{0.16365924}{6.479891 \times 10^{-5}} = 1.0 \times \dfrac{0.16365924}{6.479891 \times 10^{-5}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}} \times {\color{rgb(166,218,227)} \cancel{0.16365924}}}{{\color{rgb(166,218,227)} \cancel{0.16365924}} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-5}}}} = 1.0 \times \dfrac{0.16365924}{6.479891 \times 10^{-5}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{0.16365924}{6.479891 \times 10^{-5}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-5}}\text{ can be rewritten to }10^{5}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 0.16365924}{6.479891}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx2525.6480395\approx2.5256 \times 10^{3}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 2.5256 \times 10^{3}}\left(\dfrac{grain}{barrel}\right)$$