Convert gram / cubic meter to grain / cubic foot

Learn how to convert 1 gram / cubic meter to grain / cubic foot 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}{c u b i c f o o t})

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}{c u b i c f o o t}) = \frac{6.479891 \times 10^{- 3}}{2.8316846592} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 3}}{2.8316846592} (\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}{c u b i c f o o t})

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^{- 3}}{2.8316846592} \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^{- 3}}{2.8316846592} \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^{- 3}}{2.8316846592} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{10^{- 2}}{7.64554857984} = x \times \frac{6.479891 \times 10^{- 3}}{2.8316846592}

Cancel factors on both sides

Cancel factors

\frac{10^{- 2}}{7.64554857984} = x \times \frac{6.479891 \times {10^{- 3}}^{10^{- 1}}}{2.8316846592}

Switch sides

x \times \frac{6.479891 \times 10^{- 1}}{2.8316846592} = \frac{1.0}{7.64554857984}

Isolate

x

Multiply both sides by

(\frac{2.8316846592}{6.479891 \times 10^{- 1}})

x \times \frac{6.479891 \times 10^{- 1}}{2.8316846592} \times \frac{2.8316846592}{6.479891 \times 10^{- 1}} = \frac{1.0}{7.64554857984} \times \frac{2.8316846592}{6.479891 \times 10^{- 1}}

Cancel

x \times \frac{6.479891 \times 10^{- 1} \times 2.8316846592}{2.8316846592 \times 6.479891 \times 10^{- 1}} = \frac{1.0 \times 2.8316846592}{7.64554857984 \times 6.479891 \times 10^{- 1}}

Simplify

x = \frac{2.8316846592}{7.64554857984 \times 6.479891 \times 10^{- 1}}

Rewrite equation

\frac{1.0}{10^{- 1}} can be rewritten to 10

Rewrite

x = \frac{10.0 \times 2.8316846592}{7.64554857984 \times 6.479891}

Solve

x

x \approx 0.5715688279 \approx 5.7157 \times 10^{- 1}

Conversion Equation

1.0 (\frac{g r a m}{c u b i c m e t e r}) \approx 5.7157 \times 10^{- 1} (\frac{g r a i n}{c u b i c f o o t})

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