Convert gram / cubic mile to grain / gallon

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

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a m}{c u b i c m i l e}) = x (\frac{g r a i 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{g r a m}{c u b i c m i l e}) = \frac{10^{- 3}}{4168181825.44058} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 3}}{4168181825.44058} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{g a l l o n}) = \frac{6.479891 \times 10^{- 2}}{3.785411784} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 2}}{3.785411784} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{10^{- 3}}{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{6.479891 \times 10^{- 2}}{3.785411784} \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^{- 3}}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891 \times 10^{- 2}}{3.785411784} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{10^{- 3}}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{10^{- 3}}{4168181825.44058} = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784}

Cancel factors on both sides

Cancel factors

\frac{{10^{- 3}}^{10^{- 1}}}{4168181825.44058} = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784}

Simplify

\frac{10^{- 1}}{4168181825.44058} = x \times \frac{6.479891}{3.785411784}

Switch sides

x \times \frac{6.479891}{3.785411784} = \frac{10^{- 1}}{4168181825.44058}

Isolate

x

Multiply both sides by

(\frac{3.785411784}{6.479891})

x \times \frac{6.479891}{3.785411784} \times \frac{3.785411784}{6.479891} = \frac{10^{- 1}}{4168181825.44058} \times \frac{3.785411784}{6.479891}

Cancel

x \times \frac{6.479891 \times 3.785411784}{3.785411784 \times 6.479891} = \frac{10^{- 1} \times 3.785411784}{4168181825.44058 \times 6.479891}

Simplify

x = \frac{10^{- 1} \times 3.785411784}{4168181825.44058 \times 6.479891}

Solve

x

x \approx 1.4015183025 \times 10^{- 11} \approx 1.4015 \times 10^{- 11}

Conversion Equation

1.0 (\frac{g r a m}{c u b i c m i l e}) \approx 1.4015 \times 10^{- 11} (\frac{g r a i n}{g a l l o n})

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