Convert pound / gallon to ounce / barrel

Learn how to convert 1 pound / gallon to ounce / barrel 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{o u n c e}{b a r r e l})

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{o u n c e}{b a r r e l}) = \frac{2.8349523125 \times 10^{- 1}}{1.19240471196} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{2.8349523125 \times 10^{- 1}}{1.19240471196} (\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{o u n c e}{b a r r e l})

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{2.8349523125 \times 10^{- 1}}{1.19240471196} \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{2.8349523125 \times 10^{- 1}}{1.19240471196} \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{2.8349523125 \times 10^{- 1}}{1.19240471196} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{4.54609 \times 10^{- 2}} = x \times \frac{2.8349523125 \times 10^{- 1}}{1.19240471196}

Switch sides

x \times \frac{2.8349523125 \times 10^{- 1}}{1.19240471196} = \frac{5.0}{4.54609 \times 10^{- 2}}

Isolate

x

Multiply both sides by

(\frac{1.19240471196}{2.8349523125 \times 10^{- 1}})

x \times \frac{2.8349523125 \times 10^{- 1}}{1.19240471196} \times \frac{1.19240471196}{2.8349523125 \times 10^{- 1}} = \frac{5.0}{4.54609 \times 10^{- 2}} \times \frac{1.19240471196}{2.8349523125 \times 10^{- 1}}

Cancel

x \times \frac{2.8349523125 \times 10^{- 1} \times 1.19240471196}{1.19240471196 \times 2.8349523125 \times 10^{- 1}} = \frac{5.0 \times 1.19240471196}{4.54609 \times 10^{- 2} \times 2.8349523125 \times 10^{- 1}}

Simplify

x = \frac{5.0 \times 1.19240471196}{4.54609 \times 10^{- 2} \times 2.8349523125 \times 10^{- 1}}

Rewrite equation

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

\frac{1.0}{10^{- 1}} can be rewritten to 10

Rewrite

x = \frac{10^{2} \times 10.0 \times 5.0 \times 1.19240471196}{4.54609 \times 2.8349523125}

Simplify

x = \frac{{10.0}^{3} \times 5.0 \times 1.19240471196}{4.54609 \times 2.8349523125}

Solve

x

x \approx 462.6045507 \approx 4.626 \times 10^{2}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 4.626 \times 10^{2} (\frac{o u n c e}{b a r r e l})

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