Convert pound / cubic inch to grain / cubic yard

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

Calculation Breakdown

Set up the equation

1.0 (\frac{p o u n d}{c u b i c i n c h}) = x (\frac{g r a i n}{c u b i c y a r d})

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{p o u n d}{c u b i c i n c h}) = \frac{4.5359237}{1.6387064 \times 10^{- 4}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{4.5359237}{1.6387064 \times 10^{- 4}} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{c u b i c y a r d}) = \frac{6.479891 \times 10^{- 5}}{0.764554857984} (\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}}{0.764554857984} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{p o u n d}{c u b i c i n c h}) = x (\frac{g r a i n}{c u b i c y a r d})

Insert known values =>

1.0 \times \frac{4.5359237}{1.6387064 \times 10^{- 4}} \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}}{0.764554857984} \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{4.5359237}{1.6387064 \times 10^{- 4}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891 \times 10^{- 5}}{0.764554857984} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{4.5359237}{1.6387064 \times 10^{- 4}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891 \times 10^{- 5}}{0.764554857984} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{4.5359237}{1.6387064 \times 10^{- 4}} = x \times \frac{6.479891 \times 10^{- 5}}{0.764554857984}

Switch sides

x \times \frac{6.479891 \times 10^{- 5}}{0.764554857984} = \frac{4.5359237}{1.6387064 \times 10^{- 4}}

Isolate

x

Multiply both sides by

(\frac{0.764554857984}{6.479891 \times 10^{- 5}})

x \times \frac{6.479891 \times 10^{- 5}}{0.764554857984} \times \frac{0.764554857984}{6.479891 \times 10^{- 5}} = \frac{4.5359237}{1.6387064 \times 10^{- 4}} \times \frac{0.764554857984}{6.479891 \times 10^{- 5}}

Cancel

x \times \frac{6.479891 \times 10^{- 5} \times 0.764554857984}{0.764554857984 \times 6.479891 \times 10^{- 5}} = \frac{4.5359237 \times 0.764554857984}{1.6387064 \times 10^{- 4} \times 6.479891 \times 10^{- 5}}

Simplify

x = \frac{4.5359237 \times 0.764554857984}{1.6387064 \times 10^{- 4} \times 6.479891 \times 10^{- 5}}

Rewrite equation

\frac{1.0}{10^{- 4}} can be rewritten to 10^{4}

\frac{1.0}{10^{- 5}} can be rewritten to 10^{5}

Rewrite

x = \frac{10^{4} \times 10^{5} \times 4.5359237 \times 0.764554857984}{1.6387064 \times 6.479891}

Simplify

x = \frac{10^{9} \times 4.5359237 \times 0.764554857984}{1.6387064 \times 6.479891}

Solve

x

x = 326592000 \approx 3.2659 \times 10^{8}

Conversion Equation

1.0 (\frac{p o u n d}{c u b i c i n c h}) \approx 3.2659 \times 10^{8} (\frac{g r a i n}{c u b i c y a r d})

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