Convert ounce / barrel to grain / bushel
Learn how to convert
1
ounce / barrel to
grain / bushel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{ounce}{barrel}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{bushel}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{ounce}{barrel}\right) = {\color{rgb(89,182,91)} \dfrac{2.8349523125 \times 10^{-1}}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{2.8349523125 \times 10^{-1}}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{bushel}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{3.523907016688}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{3.523907016688}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{ounce}{barrel}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{bushel}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.8349523125 \times 10^{-1}}{1.19240471196}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{3.523907016688}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.8349523125 \times 10^{-1}}{1.19240471196}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{3.523907016688}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.8349523125 \times 10^{-1}}{1.19240471196}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-3}}{3.523907016688}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.8349523125 \times 10^{-1}}{1.19240471196} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-3}}{3.523907016688}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{2.8349523125 \times {\color{rgb(255,204,153)} \cancel{10^{-1}}}}{1.19240471196} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-3}}}}{3.523907016688}\)
\(\text{Simplify}\)
\(\dfrac{2.8349523125}{1.19240471196} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-2}}{3.523907016688}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-2}}{3.523907016688} = \dfrac{2.8349523125}{1.19240471196}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.523907016688}{6.479891 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-2}}{3.523907016688} \times \dfrac{3.523907016688}{6.479891 \times 10^{-2}} = \dfrac{2.8349523125}{1.19240471196} \times \dfrac{3.523907016688}{6.479891 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{3.523907016688}}}{{\color{rgb(166,218,227)} \cancel{3.523907016688}} \times {\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = \dfrac{2.8349523125 \times 3.523907016688}{1.19240471196 \times 6.479891 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.8349523125 \times 3.523907016688}{1.19240471196 \times 6.479891 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 2.8349523125 \times 3.523907016688}{1.19240471196 \times 6.479891}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx129.29413179\approx1.2929 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{ounce}{barrel}\right)\approx{\color{rgb(20,165,174)} 1.2929 \times 10^{2}}\left(\dfrac{grain}{bushel}\right)\)
