Convert pound / cubic meter to grain / gallon

Learn how to convert 1 pound / cubic meter to grain / gallon step by step.

Calculation Breakdown

Set up the equation

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

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 m e t e r}) = 0.5 (\frac{k i l o g r a m}{c u b i c m e t e r}) = 0.5 (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{g a l l o n}) = \frac{6.479891 \times 10^{- 2}}{3.785411784} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 2}}{3.785411784} (\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 m e t e r}) = x (\frac{g r a i n}{g a l l o n})

Insert known values =>

1.0 \times 0.5 \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^{- 2}}{3.785411784} \times (\frac{k i l o g r a m}{c u b i c m e t e r})

Or

1.0 \cdot 0.5 \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891 \times 10^{- 2}}{3.785411784} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times 0.5 \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} \times (\frac{k g}{m^{3}})

Conversion Equation

0.5 = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784}

Switch sides

x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} = 0.5

Isolate

x

Multiply both sides by

(\frac{3.785411784}{6.479891 \times 10^{- 2}})

x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} \times \frac{3.785411784}{6.479891 \times 10^{- 2}} = 0.5 \times \frac{3.785411784}{6.479891 \times 10^{- 2}}

Cancel

x \times \frac{6.479891 \times 10^{- 2} \times 3.785411784}{3.785411784 \times 6.479891 \times 10^{- 2}} = 0.5 \times \frac{3.785411784}{6.479891 \times 10^{- 2}}

Simplify

x = \frac{0.5 \times 3.785411784}{6.479891 \times 10^{- 2}}

Rewrite equation

\frac{1.0}{10^{- 2}} can be rewritten to 10^{2}

Rewrite

x = \frac{10^{2} \times 0.5 \times 3.785411784}{6.479891}

Solve

x

x \approx 29.208915582 \approx 29.2089

Conversion Equation

1.0 (\frac{p o u n d}{c u b i c m e t e r}) \approx 29.2089 (\frac{g r a i n}{g a l l o n})

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