Convert ton / cubic mile to gram / barrel
Learn how to convert
1
ton / cubic mile to
gram / barrel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{ton}{cubic \text{ } mile}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{barrel}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{ton}{cubic \text{ } mile}\right) = {\color{rgb(89,182,91)} \dfrac{10^{3}}{4168181825.44058}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{3}}{4168181825.44058}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{barrel}\right) = {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.6365924}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.6365924}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{ton}{cubic \text{ } mile}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{barrel}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{3}}{4168181825.44058}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.6365924}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{3}}{4168181825.44058}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.6365924}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{3}}{4168181825.44058}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{-2}}{1.6365924}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{3}}{4168181825.44058} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{1.6365924}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{1.6365924} = \dfrac{10^{3}}{4168181825.44058}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.6365924}{10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{1.6365924} \times \dfrac{1.6365924}{10^{-2}} = \dfrac{10^{3}}{4168181825.44058} \times \dfrac{1.6365924}{10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-2}}} \times {\color{rgb(99,194,222)} \cancel{1.6365924}}}{{\color{rgb(99,194,222)} \cancel{1.6365924}} \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}} = \dfrac{10^{3} \times 1.6365924}{4168181825.44058 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 1.6365924}{4168181825.44058 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 10^{3} \times 1.6365924}{4168181825.44058}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 1.6365924}{4168181825.44058}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000392639\approx3.9264 \times 10^{-5}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{ton}{cubic \text{ } mile}\right)\approx{\color{rgb(20,165,174)} 3.9264 \times 10^{-5}}\left(\dfrac{gram}{barrel}\right)\)
