Convert diesel to quartern

Learn how to convert 1 diesel to quartern step by step.

Calculation Breakdown

Set up the equation

1.0 (d i e s e l) = x (q u a r t e r 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 (d i e s e l) = \frac{10.0}{8.5} (c u b i c m e t e r) = \frac{10.0}{8.5} (m^{3})

Right side: 1.0 (q u a r t e r n) = 2.273045 \times 10^{- 3} (c u b i c m e t e r) = 2.273045 \times 10^{- 3} (m^{3})

Insert known values into the conversion equation to determine

x

1.0 (d i e s e l) = x (q u a r t e r n)

Insert known values =>

1.0 \times \frac{10.0}{8.5} \times (c u b i c m e t e r) = x \times 2.273045 \times 10^{- 3} \times (c u b i c m e t e r)

Or

1.0 \cdot \frac{10.0}{8.5} \cdot (m^{3}) = x \cdot 2.273045 \times 10^{- 3} \cdot (m^{3})

Cancel SI units

1.0 \times \frac{10.0}{8.5} \cdot (m^{3}) = x \times 2.273045 \times 10^{- 3} \times (m^{3})

Conversion Equation

\frac{10.0}{8.5} = x \times 2.273045 \times 10^{- 3}

Switch sides

x \times 2.273045 \times 10^{- 3} = \frac{10.0}{8.5}

Isolate

x

Multiply both sides by

(\frac{1.0}{2.273045 \times 10^{- 3}})

x \times 2.273045 \times 10^{- 3} \times \frac{1.0}{2.273045 \times 10^{- 3}} = \frac{10.0}{8.5} \times \frac{1.0}{2.273045 \times 10^{- 3}}

Cancel

x \times 2.273045 \times 10^{- 3} \times \frac{1.0}{2.273045 \times 10^{- 3}} = \frac{10.0 \times 1.0}{8.5 \times 2.273045 \times 10^{- 3}}

Simplify

x = \frac{10.0}{8.5 \times 2.273045 \times 10^{- 3}}

Rewrite equation

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

Rewrite

x = \frac{10^{3} \times 10.0}{8.5 \times 2.273045}

Simplify

x = \frac{{10.0}^{4}}{8.5 \times 2.273045}

Solve

x

x \approx 517.57470188 \approx 5.1757 \times 10^{2}

Conversion Equation

1.0 (d i e s e l) \approx 5.1757 \times 10^{2} (q u a r t e r n)

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