Convert ton / liter to ounce / cubic mile
Learn how to convert
1
ton / liter to
ounce / cubic mile
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{ton}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{ounce}{cubic \text{ } mile}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{ton}{liter}\right) = {\color{rgb(89,182,91)} 10^{6}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 10^{6}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{ounce}{cubic \text{ } mile}\right) = {\color{rgb(125,164,120)} \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{ton}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{ounce}{cubic \text{ } mile}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{6}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{6}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{6}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{6} = {\color{rgb(20,165,174)} x} \times \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058} = 10^{6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{4168181825.44058}{2.8349523125 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.8349523125 \times 10^{-2}}{4168181825.44058} \times \dfrac{4168181825.44058}{2.8349523125 \times 10^{-2}} = 10^{6} \times \dfrac{4168181825.44058}{2.8349523125 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.8349523125}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{4168181825.44058}}}{{\color{rgb(166,218,227)} \cancel{4168181825.44058}} \times {\color{rgb(255,204,153)} \cancel{2.8349523125}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = 10^{6} \times \dfrac{4168181825.44058}{2.8349523125 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{6} \times 4168181825.44058}{2.8349523125 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 10^{6} \times 4168181825.44058}{2.8349523125}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{8} \times 4168181825.44058}{2.8349523125}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1.4702828711 \times 10^{17}\approx1.4703 \times 10^{17}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{ton}{liter}\right)\approx{\color{rgb(20,165,174)} 1.4703 \times 10^{17}}\left(\dfrac{ounce}{cubic \text{ } mile}\right)\)
