Convert tonne / liter to pound / cubic inch

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

Calculation Breakdown

Set up the equation

1.0 (\frac{t o n n e}{l i t e r}) = 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{t o n n e}{l i t e r}) = \frac{1016.0469088}{10^{- 3}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{1016.0469088}{10^{- 3}} (\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{4.5359237}{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{4.5359237}{1.6387064 \times 10^{- 4}} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{1016.0469088}{10^{- 3}} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{4.5359237}{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{1016.0469088}{10^{- 3}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{4.5359237}{1.6387064 \times 10^{- 4}} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{1016.0469088}{10^{- 3}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{4.5359237}{1.6387064 \times 10^{- 4}} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{1016.0469088}{10^{- 3}} = x \times \frac{4.5359237}{1.6387064 \times 10^{- 4}}

Cancel factors on both sides

Cancel factors

\frac{1016.0469088}{10^{- 3}} = x \times \frac{4.5359237}{1.6387064 \times {10^{- 4}}^{10^{- 1}}}

Simplify

1016.0469088 = x \times \frac{4.5359237}{1.6387064 \times 10^{- 1}}

Switch sides

x \times \frac{4.5359237}{1.6387064 \times 10^{- 1}} = 1016.0469088

Isolate

x

Multiply both sides by

(\frac{1.6387064 \times 10^{- 1}}{4.5359237})

x \times \frac{4.5359237}{1.6387064 \times 10^{- 1}} \times \frac{1.6387064 \times 10^{- 1}}{4.5359237} = 1016.0469088 \times \frac{1.6387064 \times 10^{- 1}}{4.5359237}

Cancel

x \times \frac{4.5359237 \times 1.6387064 \times 10^{- 1}}{1.6387064 \times 10^{- 1} \times 4.5359237} = 1016.0469088 \times \frac{1.6387064 \times 10^{- 1}}{4.5359237}

Simplify

x = \frac{1016.0469088 \times 1.6387064 \times 10^{- 1}}{4.5359237}

Solve

x

x = 36.70702336 \approx 36.707

Conversion Equation

1.0 (\frac{t o n n e}{l i t e r}) \approx 36.707 (\frac{p o u n d}{c u b i c i n c h})

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