Convert pound / gallon to tonne / liter

Learn how to convert 1 pound / gallon to tonne / liter 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{t o n n e}{l i t e r})

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}{3.785411784 \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}{3.785411784 \times 10^{- 2}} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{t o n n e}{l i t e r}) = \frac{1016.0469088}{10^{- 3}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{1016.0469088}{10^{- 3}} (\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{t o n n e}{l i t e r})

Insert known values =>

1.0 \times \frac{5.0}{3.785411784 \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{1016.0469088}{10^{- 3}} \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}{3.785411784 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{1016.0469088}{10^{- 3}} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{5.0}{3.785411784 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{1016.0469088}{10^{- 3}} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times \frac{1016.0469088}{10^{- 3}}

Cancel factors on both sides

Cancel factors

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times \frac{1016.0469088}{{10^{- 3}}^{10^{- 1}}}

Simplify

\frac{5.0}{3.785411784} = x \times \frac{1016.0469088}{10^{- 1}}

Switch sides

x \times \frac{1016.0469088}{10^{- 1}} = \frac{5.0}{3.785411784}

Isolate

x

Multiply both sides by

(\frac{10^{- 1}}{1016.0469088})

x \times \frac{1016.0469088}{10^{- 1}} \times \frac{10^{- 1}}{1016.0469088} = \frac{5.0}{3.785411784} \times \frac{10^{- 1}}{1016.0469088}

Cancel

x \times \frac{1016.0469088 \times 10^{- 1}}{10^{- 1} \times 1016.0469088} = \frac{5.0 \times 10^{- 1}}{3.785411784 \times 1016.0469088}

Simplify

x = \frac{5.0 \times 10^{- 1}}{3.785411784 \times 1016.0469088}

Solve

x

x \approx 0.0001299999 \approx 1.3 \times 10^{- 4}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 1.3 \times 10^{- 4} (\frac{t o n n e}{l i t e r})

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