Convert gram / cubic meter to grain / barrel

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

Calculation Breakdown

Set up the equation

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

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}) = \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}})

Right 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}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \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}) = x \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})

Or

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

Cancel SI units

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

Conversion Equation

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

Cancel factors on both sides

Cancel factors

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

Switch sides

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

Isolate

x

Multiply both sides by

(\frac{0.16365924}{6.479891 \times 10^{- 3}})

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

Cancel

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

Simplify

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

Rewrite equation

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

Rewrite

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

Solve

x

x \approx 3.3034229174 \approx 3.3034

Conversion Equation

1.0 (\frac{g r a m}{c u b i c m e t e r}) \approx 3.3034 (\frac{g r a i n}{b a r r e l})

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