Convert arpent length to yin(引)

Learn how to convert 1 arpent length to yin(引) step by step.

Calculation Breakdown

Set up the equation

1.0 (a r p e n t l e n g t h) = x (y i n (引))

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

(m e t e r)

Left side: 1.0 (a r p e n t l e n g t h) = 58.5216 (m e t e r) = 58.5216 (m)

Right side: 1.0 (y i n (引)) = \frac{10^{2}}{3.0} (m e t e r) = \frac{10^{2}}{3.0} (m)

Insert known values into the conversion equation to determine

x

1.0 (a r p e n t l e n g t h) = x (y i n (引))

Insert known values =>

1.0 \times 58.5216 \times (m e t e r) = x \times \frac{10^{2}}{3.0} \times (m e t e r)

Or

1.0 \cdot 58.5216 \cdot (m) = x \cdot \frac{10^{2}}{3.0} \cdot (m)

Cancel SI units

1.0 \times 58.5216 \cdot (m) = x \times \frac{10^{2}}{3.0} \times (m)

Conversion Equation

58.5216 = x \times \frac{10^{2}}{3.0}

Switch sides

x \times \frac{10^{2}}{3.0} = 58.5216

Isolate

x

Multiply both sides by

(\frac{3.0}{10^{2}})

x \times \frac{10^{2}}{3.0} \times \frac{3.0}{10^{2}} = 58.5216 \times \frac{3.0}{10^{2}}

Cancel

x \times \frac{10^{2} \times 3.0}{3.0 \times 10^{2}} = 58.5216 \times \frac{3.0}{10^{2}}

Simplify

x = \frac{58.5216 \times 3.0}{10^{2}}

Rewrite equation

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

Rewrite

x = 10^{- 2} \times 58.5216 \times 3.0

Solve

x

x = 1.755648 \approx 1.7556

Conversion Equation

1.0 (a r p e n t l e n g t h) \approx 1.7556 (y i n (引))

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