Convert kilogram / cubic meter to grain / gallon

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

Calculation Breakdown

Set up the equation

1.0 (\frac{k i l o g r a m}{c u b i c m e t e r}) = 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 e t e r}) = 10^{- 3} (\frac{k i l o g r a m}{c u b i c m e t e r}) = 10^{- 3} (\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^{- 5}}{4.54609 \times 10^{- 3}} (\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}}{4.54609 \times 10^{- 3}} (\frac{k g}{m^{3}})

Define the values of the selected prefixes

Left side: \frac{k i l o}{1.0} = \frac{k}{1.0} = \frac{10^{3}}{1.0}

Insert known values into the conversion equation to determine

x

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

Insert known values =>

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

Cancel SI units

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

Conversion Equation

10^{- 3} \times \frac{10^{3}}{1.0} = x \times \frac{6.479891 \times 10^{- 5}}{4.54609 \times 10^{- 3}}

Simplify

1.0 = x \times \frac{6.479891 \times 10^{- 5}}{4.54609 \times 10^{- 3}}

Switch sides

x \times \frac{6.479891 \times 10^{- 5}}{4.54609 \times 10^{- 3}} = 1.0

Isolate

x

Multiply both sides by

(\frac{4.54609 \times 10^{- 3}}{6.479891 \times 10^{- 5}})

x \times \frac{6.479891 \times 10^{- 5}}{4.54609 \times 10^{- 3}} \times \frac{4.54609 \times 10^{- 3}}{6.479891 \times 10^{- 5}} = 1.0 \times \frac{4.54609 \times 10^{- 3}}{6.479891 \times 10^{- 5}}

Cancel

x \times \frac{6.479891 \times 10^{- 5} \times 4.54609 \times 10^{- 3}}{4.54609 \times 10^{- 3} \times 6.479891 \times 10^{- 5}} = 1.0 \times \frac{4.54609 \times 10^{- 3}}{6.479891 \times {10^{- 5}}^{10^{- 2}}}

Simplify

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

Rewrite equation

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

Rewrite

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

Solve

x

x \approx 70.156889985 \approx 70.1569

Conversion Equation

1.0 (\frac{k i l o g r a m}{c u b i c m e t e r}) \approx 70.1569 (\frac{g r a i n}{g a l l o n})

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