Convert grain / barrel to gram / cubic meter

Learn how to convert 1 grain / barrel to gram / cubic meter step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a i n}{b a r r e l}) = x (\frac{g r a m}{c u b i c m e 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}{b a r r e l}) = \frac{6.479891 \times 10^{- 5}}{0.16365924} (\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}}{0.16365924} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{7.64554857984} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{7.64554857984} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{6.479891 \times 10^{- 5}}{0.16365924} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{10^{- 2}}{7.64554857984} \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}}{0.16365924} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{10^{- 2}}{7.64554857984} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891 \times 10^{- 5}}{0.16365924} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{- 2}}{7.64554857984} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891 \times 10^{- 5}}{0.16365924} = x \times \frac{10^{- 2}}{7.64554857984}

Cancel factors on both sides

Cancel factors

\frac{6.479891 \times {10^{- 5}}^{10^{- 3}}}{0.16365924} = x \times \frac{10^{- 2}}{7.64554857984}

Switch sides

x \times \frac{1.0}{7.64554857984} = \frac{6.479891 \times 10^{- 3}}{0.16365924}

Isolate

x

Multiply both sides by

(\frac{7.64554857984}{1.0})

x \times \frac{1.0}{7.64554857984} \times \frac{7.64554857984}{1.0} = \frac{6.479891 \times 10^{- 3}}{0.16365924} \times \frac{7.64554857984}{1.0}

Cancel

x \times \frac{1.0 \times 7.64554857984}{7.64554857984 \times 1.0} = \frac{6.479891 \times 10^{- 3} \times 7.64554857984}{0.16365924 \times 1.0}

Simplify

x = \frac{6.479891 \times 10^{- 3} \times 7.64554857984}{0.16365924}

Solve

x

x \approx 0.3027163112 \approx 3.0272 \times 10^{- 1}

Conversion Equation

1.0 (\frac{g r a i n}{b a r r e l}) \approx 3.0272 \times 10^{- 1} (\frac{g r a m}{c u b i c m e t e r})

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