Convert grain / cubic to pound / liter

Learn how to convert 1 grain / cubic to pound / liter step by step.

Calculation Breakdown

Set up the equation

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

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 i n}{c u b i c}) = \frac{6.479891 \times 10^{- 5}}{4168181825.44058} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 5}}{4168181825.44058} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{p o u n d}{l i t e r}) = 5.0 \times 10^{2} (\frac{k i l o g r a m}{c u b i c m e t e r}) = 5.0 \times 10^{2} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times 5.0 \times 10^{2} \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{6.479891 \times 10^{- 5}}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \cdot 5.0 \times 10^{2} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \cdot (\frac{k g}{m^{3}}) = x \times 5.0 \times 10^{2} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891 \times 10^{- 5}}{4168181825.44058} = x \times 5.0 \times 10^{2}

Switch sides

x \times 5.0 \times 10^{2} = \frac{6.479891 \times 10^{- 5}}{4168181825.44058}

Isolate

x

Multiply both sides by

(\frac{1.0}{5.0 \times 10^{2}})

x \times 5.0 \times 10^{2} \times \frac{1.0}{5.0 \times 10^{2}} = \frac{6.479891 \times 10^{- 5}}{4168181825.44058} \times \frac{1.0}{5.0 \times 10^{2}}

Cancel

x \times 5.0 \times 10^{2} \times \frac{1.0}{5.0 \times 10^{2}} = \frac{6.479891 \times 10^{- 5} \times 1.0}{4168181825.44058 \times 5.0 \times 10^{2}}

Simplify

x = \frac{6.479891 \times 10^{- 5}}{4168181825.44058 \times 5.0 \times 10^{2}}

Rewrite equation

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

Rewrite

x = \frac{10^{- 2} \times 6.479891 \times 10^{- 5}}{4168181825.44058 \times 5.0}

Simplify

x = \frac{10^{- 7} \times 6.479891}{4168181825.44058 \times 5.0}

Solve

x

x \approx 3.1092170502 \times 10^{- 17} \approx 3.1092 \times 10^{- 17}

Conversion Equation

1.0 (\frac{g r a i n}{c u b i c}) \approx 3.1092 \times 10^{- 17} (\frac{p o u n d}{l i t e r})

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