Convert grain / cubic to pound / gallon

Learn how to convert 1 grain / cubic to pound / gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a i n}{c u b i c}) = x (\frac{p o u n d}{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{g r a i n}{c u b i c}) = \frac{6.479891 \times 10^{- 5}}{4168181825.44058} (\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}}{4168181825.44058} (\frac{k g}{m^{3}})

Right 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}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{g r a i n}{c u b i c}) = x (\frac{p o u n d}{g a l l o n})

Insert known values =>

1.0 \times \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \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})

Or

1.0 \cdot \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{5.0}{4.54609 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \times \frac{5.0}{4.54609 \times 10^{- 2}} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891 \times 10^{- 5}}{4168181825.44058} = x \times \frac{5.0}{4.54609 \times 10^{- 2}}

Switch sides

x \times \frac{5.0}{4.54609 \times 10^{- 2}} = \frac{6.479891 \times 10^{- 5}}{4168181825.44058}

Isolate

x

Multiply both sides by

(\frac{4.54609 \times 10^{- 2}}{5.0})

x \times \frac{5.0}{4.54609 \times 10^{- 2}} \times \frac{4.54609 \times 10^{- 2}}{5.0} = \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \times \frac{4.54609 \times 10^{- 2}}{5.0}

Cancel

x \times \frac{5.0 \times 4.54609 \times 10^{- 2}}{4.54609 \times 10^{- 2} \times 5.0} = \frac{6.479891 \times 10^{- 5} \times 4.54609 \times 10^{- 2}}{4168181825.44058 \times 5.0}

Simplify

x = \frac{6.479891 \times 10^{- 5} \times 4.54609 \times 10^{- 2}}{4168181825.44058 \times 5.0}

Solve

x

x \approx 1.413478054 \times 10^{- 16} \approx 1.4135 \times 10^{- 16}

Conversion Equation

1.0 (\frac{g r a i n}{c u b i c}) \approx 1.4135 \times 10^{- 16} (\frac{p o u n d}{g a l l o n})

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