Convert pound / cubic foot to grain / gallon

Learn how to convert 1 pound / cubic foot 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 f o o t}) = 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 f o o t}) = \frac{45.359237}{2.8316846592} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{45.359237}{2.8316846592} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{g a l l o n}) = \frac{6.479891}{454.609} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{454.609} (\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 f o o t}) = x (\frac{g r a i n}{g a l l o n})

Insert known values =>

1.0 \times \frac{45.359237}{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{6.479891}{454.609} \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{45.359237}{2.8316846592} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891}{454.609} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{45.359237}{2.8316846592} \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891}{454.609} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{45.359237}{2.8316846592} = x \times \frac{6.479891}{454.609}

Switch sides

x \times \frac{6.479891}{454.609} = \frac{45.359237}{2.8316846592}

Isolate

x

Multiply both sides by

(\frac{454.609}{6.479891})

x \times \frac{6.479891}{454.609} \times \frac{454.609}{6.479891} = \frac{45.359237}{2.8316846592} \times \frac{454.609}{6.479891}

Cancel

x \times \frac{6.479891 \times 454.609}{454.609 \times 6.479891} = \frac{45.359237 \times 454.609}{2.8316846592 \times 6.479891}

Simplify

x = \frac{45.359237 \times 454.609}{2.8316846592 \times 6.479891}

Solve

x

x \approx 1123.8055727 \approx 1.1238 \times 10^{3}

Conversion Equation

1.0 (\frac{p o u n d}{c u b i c f o o t}) \approx 1.1238 \times 10^{3} (\frac{g r a i n}{g a l l o n})

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