Convert lambda to gallon

Learn how to convert 1 lambda to gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (l a m b d a) = x (g a l l o n)

Define the base values of the selected units in relation to the SI unit

(c u b i c m e t e r)

Left side: 1.0 (l a m b d a) = 10^{- 9} (c u b i c m e t e r) = 10^{- 9} (m^{3})

Right side: 1.0 (g a l l o n) = 4.5424941408 \times 10^{- 3} (c u b i c m e t e r) = 4.5424941408 \times 10^{- 3} (m^{3})

Insert known values into the conversion equation to determine

x

1.0 (l a m b d a) = x (g a l l o n)

Insert known values =>

1.0 \times 10^{- 9} \times (c u b i c m e t e r) = x \times 4.5424941408 \times 10^{- 3} \times (c u b i c m e t e r)

Or

1.0 \cdot 10^{- 9} \cdot (m^{3}) = x \cdot 4.5424941408 \times 10^{- 3} \cdot (m^{3})

Cancel SI units

1.0 \times 10^{- 9} \cdot (m^{3}) = x \times 4.5424941408 \times 10^{- 3} \times (m^{3})

Conversion Equation

10^{- 9} = x \times 4.5424941408 \times 10^{- 3}

Cancel factors on both sides

Cancel factors

{10^{- 9}}^{10^{- 6}} = x \times 4.5424941408 \times 10^{- 3}

Simplify

10^{- 6} = x \times 4.5424941408

Switch sides

x \times 4.5424941408 = 10^{- 6}

Isolate

x

Multiply both sides by

(\frac{1.0}{4.5424941408})

x \times 4.5424941408 \times \frac{1.0}{4.5424941408} = 10^{- 6} \times \frac{1.0}{4.5424941408}

Cancel

x \times 4.5424941408 \times \frac{1.0}{4.5424941408} = 10^{- 6} \times \frac{1.0}{4.5424941408}

Simplify

x = \frac{10^{- 6}}{4.5424941408}

Solve

x

x \approx 0.0000002201 \approx 2.2014 \times 10^{- 7}

Conversion Equation

1.0 (l a m b d a) \approx 2.2014 \times 10^{- 7} (g a l l o n)

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