Convert pound / liter to ton / gallon

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

Calculation Breakdown

Set up the equation

1.0 (\frac{p o u n d}{l i t e r}) = 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}{l i t e r}) = 4.5359237 \times 10^{2} (\frac{k i l o g r a m}{c u b i c m e t e r}) = 4.5359237 \times 10^{2} (\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}{l i t e r}) = x (\frac{t o n}{g a l l o n})

Insert known values =>

1.0 \times 4.5359237 \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^{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 4.5359237 \times 10^{2} \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 4.5359237 \times 10^{2} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{6}}{4.54609} \times (\frac{k g}{m^{3}})

Conversion Equation

4.5359237 \times 10^{2} = x \times \frac{10^{6}}{4.54609}

Cancel factors on both sides

Cancel factors

4.5359237 \times 10^{2} = x \times \frac{{10^{6}}^{10^{4}}}{4.54609}

Simplify

4.5359237 = x \times \frac{10^{4}}{4.54609}

Switch sides

x \times \frac{10^{4}}{4.54609} = 4.5359237

Isolate

x

Multiply both sides by

(\frac{4.54609}{10^{4}})

x \times \frac{10^{4}}{4.54609} \times \frac{4.54609}{10^{4}} = 4.5359237 \times \frac{4.54609}{10^{4}}

Cancel

x \times \frac{10^{4} \times 4.54609}{4.54609 \times 10^{4}} = 4.5359237 \times \frac{4.54609}{10^{4}}

Simplify

x = \frac{4.5359237 \times 4.54609}{10^{4}}

Rewrite equation

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

Rewrite

x = 10^{- 4} \times 4.5359237 \times 4.54609

Solve

x

x \approx 0.0020620717 \approx 2.0621 \times 10^{- 3}

Conversion Equation

1.0 (\frac{p o u n d}{l i t e r}) \approx 2.0621 \times 10^{- 3} (\frac{t o n}{g a l l o n})

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