Convert pound / gallon to tonne / barrel
Learn how to convert
1
pound / gallon to
tonne / barrel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{tonne}{barrel}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{gallon}\right) = {\color{rgb(89,182,91)} \dfrac{5.0}{3.785411784 \times 10^{-2}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{5.0}{3.785411784 \times 10^{-2}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{tonne}{barrel}\right) = {\color{rgb(125,164,120)} \dfrac{10160.469088}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{10160.469088}{1.19240471196}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{gallon}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{tonne}{barrel}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{5.0}{3.785411784 \times 10^{-2}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10160.469088}{1.19240471196}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{5.0}{3.785411784 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10160.469088}{1.19240471196}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{5.0}{3.785411784 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10160.469088}{1.19240471196}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{5.0}{3.785411784 \times 10^{-2}} = {\color{rgb(20,165,174)} x} \times \dfrac{10160.469088}{1.19240471196}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10160.469088}{1.19240471196} = \dfrac{5.0}{3.785411784 \times 10^{-2}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.19240471196}{10160.469088}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10160.469088}{1.19240471196} \times \dfrac{1.19240471196}{10160.469088} = \dfrac{5.0}{3.785411784 \times 10^{-2}} \times \dfrac{1.19240471196}{10160.469088}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10160.469088}} \times {\color{rgb(99,194,222)} \cancel{1.19240471196}}}{{\color{rgb(99,194,222)} \cancel{1.19240471196}} \times {\color{rgb(255,204,153)} \cancel{10160.469088}}} = \dfrac{5.0 \times 1.19240471196}{3.785411784 \times 10^{-2} \times 10160.469088}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{5.0 \times 1.19240471196}{3.785411784 \times 10^{-2} \times 10160.469088}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 5.0 \times 1.19240471196}{3.785411784 \times 10160.469088}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0155012528\approx1.5501 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{gallon}\right)\approx{\color{rgb(20,165,174)} 1.5501 \times 10^{-2}}\left(\dfrac{tonne}{barrel}\right)\)
