Convert gallon to lambda

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

Calculation Breakdown

Set up the equation

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

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 (g a l l o n) = 4.54609 \times 10^{- 3} (c u b i c m e t e r) = 4.54609 \times 10^{- 3} (m^{3})

Right 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})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times 4.54609 \times 10^{- 3} \times (c u b i c m e t e r) = x \times 10^{- 9} \times (c u b i c m e t e r)

Or

1.0 \cdot 4.54609 \times 10^{- 3} \cdot (m^{3}) = x \cdot 10^{- 9} \cdot (m^{3})

Cancel SI units

1.0 \times 4.54609 \times 10^{- 3} \cdot (m^{3}) = x \times 10^{- 9} \times (m^{3})

Conversion Equation

4.54609 \times 10^{- 3} = x \times 10^{- 9}

Cancel factors on both sides

Cancel factors

4.54609 \times 10^{- 3} = x \times {10^{- 9}}^{10^{- 6}}

Simplify

4.54609 = x \times 10^{- 6}

Switch sides

x \times 10^{- 6} = 4.54609

Isolate

x

Multiply both sides by

(\frac{1.0}{10^{- 6}})

x \times 10^{- 6} \times \frac{1.0}{10^{- 6}} = 4.54609 \times \frac{1.0}{10^{- 6}}

Cancel

x \times 10^{- 6} \times \frac{1.0}{10^{- 6}} = 4.54609 \times \frac{1.0}{10^{- 6}}

Simplify

x = \frac{4.54609}{10^{- 6}}

Rewrite equation

\frac{1.0}{10^{- 6}} can be rewritten to 10^{6}

Rewrite

x = 10^{6} \times 4.54609

Solve

x

x = 4546090 \approx 4.5461 \times 10^{6}

Conversion Equation

1.0 (g a l l o n) \approx 4.5461 \times 10^{6} (l a m b d a)

View All Examples