Convert pound / gallon to pound / cubic inch

Learn how to convert 1 pound / gallon to pound / cubic inch 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 i n c h})

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}{4.54609 \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}{4.54609 \times 10^{- 2}} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{p o u n d}{c u b i c i n c h}) = \frac{5.0}{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{5.0}{1.6387064 \times 10^{- 4}} (\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 i n c h})

Insert known values =>

1.0 \times \frac{5.0}{4.54609 \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}{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})

Or

1.0 \cdot \frac{5.0}{4.54609 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{5.0}{1.6387064 \times 10^{- 4}} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{5.0}{4.54609 \times 10^{- 2}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{5.0}{1.6387064 \times 10^{- 4}} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{4.54609 \times 10^{- 2}} = x \times \frac{5.0}{1.6387064 \times 10^{- 4}}

Cancel factors on both sides

Cancel factors

\frac{5.0}{4.54609 \times 10^{- 2}} = x \times \frac{5.0}{1.6387064 \times {10^{- 4}}^{10^{- 2}}}

Simplify

\frac{1.0}{4.54609} = x \times \frac{1.0}{1.6387064 \times 10^{- 2}}

Switch sides

x \times \frac{1.0}{1.6387064 \times 10^{- 2}} = \frac{1.0}{4.54609}

Isolate

x

Multiply both sides by

(\frac{1.6387064 \times 10^{- 2}}{1.0})

x \times \frac{1.0}{1.6387064 \times 10^{- 2}} \times \frac{1.6387064 \times 10^{- 2}}{1.0} = \frac{1.0}{4.54609} \times \frac{1.6387064 \times 10^{- 2}}{1.0}

Cancel

x \times \frac{1.0 \times 1.6387064 \times 10^{- 2}}{1.6387064 \times 10^{- 2} \times 1.0} = \frac{1.0 \times 1.6387064 \times 10^{- 2}}{4.54609 \times 1.0}

Simplify

x = \frac{1.6387064 \times 10^{- 2}}{4.54609}

Solve

x

x \approx 0.0036046501 \approx 3.6047 \times 10^{- 3}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 3.6047 \times 10^{- 3} (\frac{p o u n d}{c u b i c i n c h})

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