Convert gram / cubic mile to pound / cubic inch

Learn how to convert 1 gram / cubic mile to pound / cubic inch step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a m}{c u b i c m i l e}) = 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{g r a m}{c u b i c m i l e}) = \frac{10^{- 3}}{4168181825.44058} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 3}}{4168181825.44058} (\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{g r a m}{c u b i c m i l e}) = x (\frac{p o u n d}{c u b i c i n c h})

Insert known values =>

1.0 \times \frac{10^{- 3}}{4168181825.44058} \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{10^{- 3}}{4168181825.44058} \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{10^{- 3}}{4168181825.44058} \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{10^{- 3}}{4168181825.44058} = x \times \frac{5.0}{1.6387064 \times 10^{- 4}}

Switch sides

x \times \frac{5.0}{1.6387064 \times 10^{- 4}} = \frac{10^{- 3}}{4168181825.44058}

Isolate

x

Multiply both sides by

(\frac{1.6387064 \times 10^{- 4}}{5.0})

x \times \frac{5.0}{1.6387064 \times 10^{- 4}} \times \frac{1.6387064 \times 10^{- 4}}{5.0} = \frac{10^{- 3}}{4168181825.44058} \times \frac{1.6387064 \times 10^{- 4}}{5.0}

Cancel

x \times \frac{5.0 \times 1.6387064 \times 10^{- 4}}{1.6387064 \times 10^{- 4} \times 5.0} = \frac{10^{- 3} \times 1.6387064 \times 10^{- 4}}{4168181825.44058 \times 5.0}

Simplify

x = \frac{10^{- 3} \times 1.6387064 \times 10^{- 4}}{4168181825.44058 \times 5.0}

Solve

x

x \approx 7.8629314585 \times 10^{- 18} \approx 7.8629 \times 10^{- 18}

Conversion Equation

1.0 (\frac{g r a m}{c u b i c m i l e}) \approx 7.8629 \times 10^{- 18} (\frac{p o u n d}{c u b i c i n c h})

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