Convert dan(市石) to gallon

Learn how to convert 1 dan(市石) to gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (d a n (市 石)) = 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 (d a n (市 石)) = 10^{- 1} (c u b i c m e t e r) = 10^{- 1} (m^{3})

Right side: 1.0 (g a l l o n) = 4.621152048 \times 10^{- 3} (c u b i c m e t e r) = 4.621152048 \times 10^{- 3} (m^{3})

Insert known values into the conversion equation to determine

x

1.0 (d a n (市 石)) = x (g a l l o n)

Insert known values =>

1.0 \times 10^{- 1} \times (c u b i c m e t e r) = x \times 4.621152048 \times 10^{- 3} \times (c u b i c m e t e r)

Or

1.0 \cdot 10^{- 1} \cdot (m^{3}) = x \cdot 4.621152048 \times 10^{- 3} \cdot (m^{3})

Cancel SI units

1.0 \times 10^{- 1} \cdot (m^{3}) = x \times 4.621152048 \times 10^{- 3} \times (m^{3})

Conversion Equation

10^{- 1} = x \times 4.621152048 \times 10^{- 3}

Cancel factors on both sides

Cancel factors

10^{- 1} = x \times 4.621152048 \times {10^{- 3}}^{10^{- 2}}

Simplify

1.0 = x \times 4.621152048 \times 10^{- 2}

Switch sides

x \times 4.621152048 \times 10^{- 2} = 1.0

Isolate

x

Multiply both sides by

(\frac{1.0}{4.621152048 \times 10^{- 2}})

x \times 4.621152048 \times 10^{- 2} \times \frac{1.0}{4.621152048 \times 10^{- 2}} = \times \frac{1.0}{4.621152048 \times 10^{- 2}}

Cancel

x \times 4.621152048 \times 10^{- 2} \times \frac{1.0}{4.621152048 \times 10^{- 2}} = \frac{1.0}{4.621152048 \times 10^{- 2}}

Simplify

x = \frac{1.0}{4.621152048 \times 10^{- 2}}

Rewrite equation

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

Rewrite

x = \frac{10^{2}}{4.621152048}

Solve

x

x \approx 21.639625566 \approx 21.6396

Conversion Equation

1.0 (d a n (市 石)) \approx 21.6396 (g a l l o n)

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