Convert grain / cubic inch to pound / barrel

Learn how to convert 1 grain / cubic inch to pound / barrel step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a i n}{c u b i c i n c h}) = x (\frac{p o u n d}{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 i n c h}) = \frac{6.479891}{1.6387064} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{1.6387064} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{p o u n d}{b a r r e l}) = \frac{5.0}{1.19240471196} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{5.0}{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 i n c h}) = x (\frac{p o u n d}{b a r r e l})

Insert known values =>

1.0 \times \frac{6.479891}{1.6387064} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{5.0}{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}{1.6387064} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{5.0}{1.19240471196} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891}{1.6387064} \cdot (\frac{k g}{m^{3}}) = x \times \frac{5.0}{1.19240471196} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891}{1.6387064} = x \times \frac{5.0}{1.19240471196}

Switch sides

x \times \frac{5.0}{1.19240471196} = \frac{6.479891}{1.6387064}

Isolate

x

Multiply both sides by

(\frac{1.19240471196}{5.0})

x \times \frac{5.0}{1.19240471196} \times \frac{1.19240471196}{5.0} = \frac{6.479891}{1.6387064} \times \frac{1.19240471196}{5.0}

Cancel

x \times \frac{5.0 \times 1.19240471196}{1.19240471196 \times 5.0} = \frac{6.479891 \times 1.19240471196}{1.6387064 \times 5.0}

Simplify

x = \frac{6.479891 \times 1.19240471196}{1.6387064 \times 5.0}

Solve

x

x \approx 0.9430185372 \approx 9.4302 \times 10^{- 1}

Conversion Equation

1.0 (\frac{g r a i n}{c u b i c i n c h}) \approx 9.4302 \times 10^{- 1} (\frac{p o u n d}{b a r r e l})

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