Convert pound / cubic foot to gram / barrel

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

Calculation Breakdown

Set up the equation

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

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}{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}})

Right side: 1.0 (\frac{g r a m}{b a r r e l}) = \frac{10^{- 2}}{1.6365924} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{1.6365924} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \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}) = x \times \frac{10^{- 2}}{1.6365924} \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}{0.28316846592} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{10^{- 2}}{1.6365924} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{5.0}{0.28316846592} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{- 2}}{1.6365924} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{5.0}{0.28316846592} = x \times \frac{10^{- 2}}{1.6365924}

Switch sides

x \times \frac{10^{- 2}}{1.6365924} = \frac{5.0}{0.28316846592}

Isolate

x

Multiply both sides by

(\frac{1.6365924}{10^{- 2}})

x \times \frac{10^{- 2}}{1.6365924} \times \frac{1.6365924}{10^{- 2}} = \frac{5.0}{0.28316846592} \times \frac{1.6365924}{10^{- 2}}

Cancel

x \times \frac{10^{- 2} \times 1.6365924}{1.6365924 \times 10^{- 2}} = \frac{5.0 \times 1.6365924}{0.28316846592 \times 10^{- 2}}

Simplify

x = \frac{5.0 \times 1.6365924}{0.28316846592 \times 10^{- 2}}

Rewrite equation

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

Rewrite

x = \frac{10^{2} \times 5.0 \times 1.6365924}{0.28316846592}

Solve

x

x \approx 2889.7857582 \approx 2.8898 \times 10^{3}

Conversion Equation

1.0 (\frac{p o u n d}{c u b i c f o o t}) \approx 2.8898 \times 10^{3} (\frac{g r a m}{b a r r e l})

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