Convert pound / gallon to ton / liter

Learn how to convert 1 pound / gallon to ton / 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}{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}{l i t e r}) = 10^{6} (\frac{k i l o g r a m}{c u b i c m e t e r}) = 10^{6} (\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}{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 10^{6} \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 10^{6} \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 10^{6} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times 10^{6}

Switch sides

x \times 10^{6} = \frac{5.0}{3.785411784 \times 10^{- 2}}

Isolate

x

Multiply both sides by

(\frac{1.0}{10^{6}})

x \times 10^{6} \times \frac{1.0}{10^{6}} = \frac{5.0}{3.785411784 \times 10^{- 2}} \times \frac{1.0}{10^{6}}

Cancel

x \times 10^{6} \times \frac{1.0}{10^{6}} = \frac{5.0 \times 1.0}{3.785411784 \times 10^{- 2} \times {10^{6}}^{10^{4}}}

Simplify

x = \frac{5.0}{3.785411784 \times 10^{4}}

Rewrite equation

\frac{1.0}{10^{4}} can be rewritten to 10^{- 4}

Rewrite

x = \frac{10^{- 4} \times 5.0}{3.785411784}

Solve

x

x \approx 0.000132086 \approx 1.3209 \times 10^{- 4}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 1.3209 \times 10^{- 4} (\frac{t o n}{l i t e r})

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