Convert pound / gallon to gram / barrel

Learn how to convert 1 pound / gallon to gram / 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{g r a m}{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{g r a m}{b a r r e l}) = \frac{10^{- 2}}{1.6365924} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{1.6365924} (\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{g r a m}{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{10^{- 2}}{1.6365924} \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{10^{- 2}}{1.6365924} \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{10^{- 2}}{1.6365924} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{4.54609 \times 10^{- 2}} = x \times \frac{10^{- 2}}{1.6365924}

Switch sides

x \times \frac{10^{- 2}}{1.6365924} = \frac{5.0}{4.54609 \times 10^{- 2}}

Isolate

x

Multiply both sides by

(\frac{1.6365924}{10^{- 2}})

x \times \frac{10^{- 2}}{1.6365924} \times \frac{1.6365924}{10^{- 2}} = \frac{5.0}{4.54609 \times 10^{- 2}} \times \frac{1.6365924}{10^{- 2}}

Cancel

x \times \frac{10^{- 2} \times 1.6365924}{1.6365924 \times 10^{- 2}} = \frac{5.0 \times 1.6365924}{4.54609 \times 10^{- 2} \times 10^{- 2}}

Simplify

x = \frac{5.0 \times 1.6365924}{4.54609 \times 10^{- 2} \times 10^{- 2}}

Rewrite equation

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

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

Rewrite

x = \frac{10^{2} \times 10^{2} \times 5.0 \times 1.6365924}{4.54609}

Simplify

x = \frac{10^{4} \times 5.0 \times 1.6365924}{4.54609}

Solve

x

x = 18000 = 1.8 \times 10^{4}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) = 1.8 \times 10^{4} (\frac{g r a m}{b a r r e l})

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