Convert grain / liter to gram / barrel
Learn how to convert
1
grain / liter to
gram / barrel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{barrel}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{liter}\right) = {\color{rgb(89,182,91)} 6.479891 \times 10^{-2}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 6.479891 \times 10^{-2}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{barrel}\right) = {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{barrel}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-2}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.19240471196}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 6.479891 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.19240471196}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.19240471196}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(6.479891 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{1.19240471196}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(6.479891 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-2}}}}{1.19240471196}\)
\(\text{Simplify}\)
\(6.479891 = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.19240471196}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.19240471196} = 6.479891\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.19240471196}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.19240471196} \times \dfrac{1.19240471196}{1.0} = 6.479891 \times \dfrac{1.19240471196}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{1.19240471196}}}{{\color{rgb(99,194,222)} \cancel{1.19240471196}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = 6.479891 \times \dfrac{1.19240471196}{1.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = 6.479891 \times 1.19240471196\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx7.7266525614\approx7.7267\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{liter}\right)\approx{\color{rgb(20,165,174)} 7.7267}\left(\dfrac{gram}{barrel}\right)\)
