Convert pound / gallon to gram / cubic mile

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

Calculation Breakdown

Set up the equation

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

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}{g a l l o n}) = \frac{5.0}{4.54609 \times 10^{- 2}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{5.0}{4.54609 \times 10^{- 2}} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a m}{c u b i c m i l e}) = \frac{10^{- 3}}{4168181825.44058} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 3}}{4168181825.44058} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{5.0}{4.54609 \times 10^{- 2}} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{10^{- 3}}{4168181825.44058} \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{5.0}{4.54609 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{10^{- 3}}{4168181825.44058} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{5.0}{4.54609 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{- 3}}{4168181825.44058} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{4.54609 \times 10^{- 2}} = x \times \frac{10^{- 3}}{4168181825.44058}

Switch sides

x \times \frac{10^{- 3}}{4168181825.44058} = \frac{5.0}{4.54609 \times 10^{- 2}}

Isolate

x

Multiply both sides by

(\frac{4168181825.44058}{10^{- 3}})

x \times \frac{10^{- 3}}{4168181825.44058} \times \frac{4168181825.44058}{10^{- 3}} = \frac{5.0}{4.54609 \times 10^{- 2}} \times \frac{4168181825.44058}{10^{- 3}}

Cancel

x \times \frac{10^{- 3} \times 4168181825.44058}{4168181825.44058 \times 10^{- 3}} = \frac{5.0 \times 4168181825.44058}{4.54609 \times 10^{- 2} \times 10^{- 3}}

Simplify

x = \frac{5.0 \times 4168181825.44058}{4.54609 \times 10^{- 2} \times 10^{- 3}}

Rewrite equation

\frac{1.0}{10^{- 2}} can be rewritten to 10^{2}

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

Rewrite

x = \frac{10^{2} \times 10^{3} \times 5.0 \times 4168181825.44058}{4.54609}

Simplify

x = \frac{10^{5} \times 5.0 \times 4168181825.44058}{4.54609}

Solve

x

x \approx 4.5843591146 \times 10^{14} \approx 4.5844 \times 10^{14}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 4.5844 \times 10^{14} (\frac{g r a m}{c u b i c m i l e})

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