Convert pound / gallon to ton / cubic inch

Learn how to convert 1 pound / gallon to ton / 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{t o n}{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}{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{t o n}{c u b i c i n c h}) = \frac{10^{3}}{1.6387064 \times 10^{- 5}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{3}}{1.6387064 \times 10^{- 5}} (\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{t o n}{c u b i c i n c h})

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{10^{3}}{1.6387064 \times 10^{- 5}} \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{10^{3}}{1.6387064 \times 10^{- 5}} \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{10^{3}}{1.6387064 \times 10^{- 5}} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times \frac{10^{3}}{1.6387064 \times 10^{- 5}}

Cancel factors on both sides

Cancel factors

\frac{5.0}{3.785411784 \times 10^{- 2}} = x \times \frac{10^{3}}{1.6387064 \times {10^{- 5}}^{10^{- 3}}}

Simplify

\frac{5.0}{3.785411784} = x \times \frac{10^{3}}{1.6387064 \times 10^{- 3}}

Switch sides

x \times \frac{10^{3}}{1.6387064 \times 10^{- 3}} = \frac{5.0}{3.785411784}

Isolate

x

Multiply both sides by

(\frac{1.6387064 \times 10^{- 3}}{10^{3}})

x \times \frac{10^{3}}{1.6387064 \times 10^{- 3}} \times \frac{1.6387064 \times 10^{- 3}}{10^{3}} = \frac{5.0}{3.785411784} \times \frac{1.6387064 \times 10^{- 3}}{10^{3}}

Cancel

x \times \frac{10^{3} \times 1.6387064 \times 10^{- 3}}{1.6387064 \times 10^{- 3} \times 10^{3}} = \frac{5.0 \times 1.6387064 \times 10^{- 3}}{3.785411784 \times 10^{3}}

Simplify

x = \frac{5.0 \times 1.6387064 \times 10^{- 3}}{3.785411784 \times 10^{3}}

Rewrite equation

\frac{1.0}{10^{3}} can be rewritten to 10^{- 3}

Rewrite

x = \frac{10^{- 3} \times 5.0 \times 1.6387064 \times 10^{- 3}}{3.785411784}

Simplify

x = \frac{10^{- 6} \times 5.0 \times 1.6387064}{3.785411784}

Solve

x

x \approx 0.0000021645 \approx 2.1645 \times 10^{- 6}

Conversion Equation

1.0 (\frac{p o u n d}{g a l l o n}) \approx 2.1645 \times 10^{- 6} (\frac{t o n}{c u b i c i n c h})

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