Convert pound / gallon to pound / cubic foot

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

Calculation Breakdown

Set up the equation

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

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}{g a l l o n}) = \frac{5.0}{3.785411784 \times 10^{- 2}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{5.0}{3.785411784 \times 10^{- 2}} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{p o u n d}{c u b i c f o o t}) = \frac{5.0}{0.28316846592} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{5.0}{0.28316846592} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{5.0}{3.785411784 \times 10^{- 2}} \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}{0.28316846592} \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{5.0}{3.785411784 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{5.0}{0.28316846592} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{5.0}{3.785411784 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{5.0}{0.28316846592} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times \frac{5.0}{0.28316846592}

Cancel factors on both sides

Cancel factors

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times \frac{5.0}{0.28316846592}

Switch sides

x \times \frac{1.0}{0.28316846592} = \frac{1.0}{3.785411784 \times 10^{- 2}}

Isolate

x

Multiply both sides by

(\frac{0.28316846592}{1.0})

x \times \frac{1.0}{0.28316846592} \times \frac{0.28316846592}{1.0} = \frac{1.0}{3.785411784 \times 10^{- 2}} \times \frac{0.28316846592}{1.0}

Cancel

x \times \frac{1.0 \times 0.28316846592}{0.28316846592 \times 1.0} = \frac{1.0 \times 0.28316846592}{3.785411784 \times 10^{- 2} \times 1.0}

Simplify

x = \frac{0.28316846592}{3.785411784 \times 10^{- 2}}

Rewrite equation

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

Rewrite

x = \frac{10^{2} \times 0.28316846592}{3.785411784}

Solve

x

x \approx 7.4805194805 \approx 7.4805

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 7.4805 (\frac{p o u n d}{c u b i c f o o t})

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