Convert pound / gallon to grain / barrel

Learn how to convert 1 pound / gallon to grain / 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 i n}{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 i n}{b a r r e l}) = \frac{6.479891 \times 10^{- 5}}{0.119240471196} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 5}}{0.119240471196} (\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 i n}{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{6.479891 \times 10^{- 5}}{0.119240471196} \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{6.479891 \times 10^{- 5}}{0.119240471196} \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{6.479891 \times 10^{- 5}}{0.119240471196} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{4.54609 \times 10^{- 2}} = x \times \frac{6.479891 \times 10^{- 5}}{0.119240471196}

Switch sides

x \times \frac{6.479891 \times 10^{- 5}}{0.119240471196} = \frac{5.0}{4.54609 \times 10^{- 2}}

Isolate

x

Multiply both sides by

(\frac{0.119240471196}{6.479891 \times 10^{- 5}})

x \times \frac{6.479891 \times 10^{- 5}}{0.119240471196} \times \frac{0.119240471196}{6.479891 \times 10^{- 5}} = \frac{5.0}{4.54609 \times 10^{- 2}} \times \frac{0.119240471196}{6.479891 \times 10^{- 5}}

Cancel

x \times \frac{6.479891 \times 10^{- 5} \times 0.119240471196}{0.119240471196 \times 6.479891 \times 10^{- 5}} = \frac{5.0 \times 0.119240471196}{4.54609 \times 10^{- 2} \times 6.479891 \times 10^{- 5}}

Simplify

x = \frac{5.0 \times 0.119240471196}{4.54609 \times 10^{- 2} \times 6.479891 \times 10^{- 5}}

Rewrite equation

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

\frac{1.0}{10^{- 5}} can be rewritten to 10^{5}

Rewrite

x = \frac{10^{2} \times 10^{5} \times 5.0 \times 0.119240471196}{4.54609 \times 6.479891}

Simplify

x = \frac{10^{7} \times 5.0 \times 0.119240471196}{4.54609 \times 6.479891}

Solve

x

x \approx 202389.49093 \approx 2.0239 \times 10^{5}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 2.0239 \times 10^{5} (\frac{g r a i n}{b a r r e l})

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