Convert grain / cubic foot to gram / barrel

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

Calculation Breakdown

Set up the equation

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

Right side: 1.0 (\frac{g r a m}{b a r r e l}) = \frac{10^{- 2}}{1.19240471196} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{1.19240471196} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \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}) = x \times \frac{10^{- 2}}{1.19240471196} \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^{- 3}}{2.8316846592} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{10^{- 2}}{1.19240471196} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891 \times 10^{- 3}}{2.8316846592} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{- 2}}{1.19240471196} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891 \times 10^{- 3}}{2.8316846592} = x \times \frac{10^{- 2}}{1.19240471196}

Cancel factors on both sides

Cancel factors

\frac{6.479891 \times {10^{- 3}}^{10^{- 1}}}{2.8316846592} = x \times \frac{10^{- 2}}{1.19240471196}

Switch sides

x \times \frac{1.0}{1.19240471196} = \frac{6.479891 \times 10^{- 1}}{2.8316846592}

Isolate

x

Multiply both sides by

(\frac{1.19240471196}{1.0})

x \times \frac{1.0}{1.19240471196} \times \frac{1.19240471196}{1.0} = \frac{6.479891 \times 10^{- 1}}{2.8316846592} \times \frac{1.19240471196}{1.0}

Cancel

x \times \frac{1.0 \times 1.19240471196}{1.19240471196 \times 1.0} = \frac{6.479891 \times 10^{- 1} \times 1.19240471196}{2.8316846592 \times 1.0}

Simplify

x = \frac{6.479891 \times 10^{- 1} \times 1.19240471196}{2.8316846592}

Solve

x

x \approx 0.2728641601 \approx 2.7286 \times 10^{- 1}

Conversion Equation

1.0 (\frac{g r a i n}{c u b i c f o o t}) \approx 2.7286 \times 10^{- 1} (\frac{g r a m}{b a r r e l})

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