Convert ton / barrel to ton / gallon

Learn how to convert 1 ton / barrel to ton / gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{t o n}{b a r r e l}) = 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{t o n}{b a r r e l}) = \frac{10^{4}}{1.6365924} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{4}}{1.6365924} (\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{t o n}{b a r r e l}) = x (\frac{t o n}{g a l l o n})

Insert known values =>

1.0 \times \frac{10^{4}}{1.6365924} \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{10^{4}}{1.6365924} \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{10^{4}}{1.6365924} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{6}}{4.54609} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{10^{4}}{1.6365924} = x \times \frac{10^{6}}{4.54609}

Cancel factors on both sides

Cancel factors

\frac{10^{4}}{1.6365924} = x \times \frac{{10^{6}}^{10^{2}}}{4.54609}

Switch sides

x \times \frac{10^{2}}{4.54609} = \frac{1.0}{1.6365924}

Isolate

x

Multiply both sides by

(\frac{4.54609}{10^{2}})

x \times \frac{10^{2}}{4.54609} \times \frac{4.54609}{10^{2}} = \frac{1.0}{1.6365924} \times \frac{4.54609}{10^{2}}

Cancel

x \times \frac{10^{2} \times 4.54609}{4.54609 \times 10^{2}} = \frac{1.0 \times 4.54609}{1.6365924 \times 10^{2}}

Simplify

x = \frac{4.54609}{1.6365924 \times 10^{2}}

Rewrite equation

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

Rewrite

x = \frac{10^{- 2} \times 4.54609}{1.6365924}

Solve

x

x \approx 0.0277777778 \approx 2.7778 \times 10^{- 2}

Conversion Equation

1.0 (\frac{t o n}{b a r r e l}) \approx 2.7778 \times 10^{- 2} (\frac{t o n}{g a l l o n})

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