Convert pound / cubic mile to ton / gallon

Learn how to convert 1 pound / cubic mile to ton / gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{p o u n d}{c u b i c m i l e}) = x (\frac{t o n}{g a l l o n})

Define the base values of the selected units in relation to the SI unit

(\frac{k i l o g r a m}{c u b i c m e t e r})

Left side: 1.0 (\frac{p o u n d}{c u b i c m i l e}) = \frac{0.45359237}{4168181825.44058} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{0.45359237}{4168181825.44058} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{t o n}{g a l l o n}) = \frac{10^{6}}{4.54609} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{6}}{4.54609} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{p o u n d}{c u b i c m i l e}) = x (\frac{t o n}{g a l l o n})

Insert known values =>

1.0 \times \frac{0.45359237}{4168181825.44058} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{10^{6}}{4.54609} \times (\frac{k i l o g r a m}{c u b i c m e t e r})

Or

1.0 \cdot \frac{0.45359237}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{10^{6}}{4.54609} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{0.45359237}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{6}}{4.54609} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{0.45359237}{4168181825.44058} = x \times \frac{10^{6}}{4.54609}

Switch sides

x \times \frac{10^{6}}{4.54609} = \frac{0.45359237}{4168181825.44058}

Isolate

x

Multiply both sides by

(\frac{4.54609}{10^{6}})

x \times \frac{10^{6}}{4.54609} \times \frac{4.54609}{10^{6}} = \frac{0.45359237}{4168181825.44058} \times \frac{4.54609}{10^{6}}

Cancel

x \times \frac{10^{6} \times 4.54609}{4.54609 \times 10^{6}} = \frac{0.45359237 \times 4.54609}{4168181825.44058 \times 10^{6}}

Simplify

x = \frac{0.45359237 \times 4.54609}{4168181825.44058 \times 10^{6}}

Rewrite equation

\frac{1.0}{10^{6}} can be rewritten to 10^{- 6}

Rewrite

x = \frac{10^{- 6} \times 0.45359237 \times 4.54609}{4168181825.44058}

Solve

x

x \approx 4.9471731889 \times 10^{- 16} \approx 4.9472 \times 10^{- 16}

Conversion Equation

1.0 (\frac{p o u n d}{c u b i c m i l e}) \approx 4.9472 \times 10^{- 16} (\frac{t o n}{g a l l o n})

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