Convert grain / gallon to grain / liter

Learn how to convert 1 grain / gallon to grain / liter step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a i n}{g a l l o n}) = x (\frac{g r a i n}{l i t e r})

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}{g a l l o n}) = \frac{6.479891}{454.609} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{454.609} (\frac{k g}{m^{3}})

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

Insert known values =>

1.0 \times \frac{6.479891}{454.609} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times 6.479891 \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}{454.609} \cdot (\frac{k g}{m^{3}}) = x \cdot 6.479891 \times 10^{- 2} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891}{454.609} \cdot (\frac{k g}{m^{3}}) = x \times 6.479891 \times 10^{- 2} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891}{454.609} = x \times 6.479891 \times 10^{- 2}

Cancel factors on both sides

Cancel factors

\frac{6.479891}{454.609} = x \times 6.479891 \times 10^{- 2}

Simplify

\frac{1.0}{454.609} = x \times 10^{- 2}

Switch sides

x \times 10^{- 2} = \frac{1.0}{454.609}

Isolate

x

Multiply both sides by

(\frac{1.0}{10^{- 2}})

x \times 10^{- 2} \times \frac{1.0}{10^{- 2}} = \frac{1.0}{454.609} \times \frac{1.0}{10^{- 2}}

Cancel

x \times 10^{- 2} \times \frac{1.0}{10^{- 2}} = \frac{1.0 \times 1.0}{454.609 \times 10^{- 2}}

Simplify

x = \frac{1.0}{454.609 \times 10^{- 2}}

Rewrite equation

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

Rewrite

x = \frac{10^{2}}{454.609}

Solve

x

x \approx 0.2199692483 \approx 2.1997 \times 10^{- 1}

Conversion Equation

1.0 (\frac{g r a i n}{g a l l o n}) \approx 2.1997 \times 10^{- 1} (\frac{g r a i n}{l i t e r})

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