Convert minute of arc to circle

Learn how to convert 1 minute of arc to circle step by step.

Calculation Breakdown

Set up the equation

1.0 (m i n u t e o f a r c) = x (c i r c l e)

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

(r a d i a n)

Left side: 1.0 (m i n u t e o f a r c) = \frac{π}{1.08 \times 10^{4}} (r a d i a n) = \frac{π}{1.08 \times 10^{4}} (r a d)

Right side: 1.0 (c i r c l e) = 2.0 \times π (r a d i a n) = 2.0 \times π (r a d)

Insert known values into the conversion equation to determine

x

1.0 (m i n u t e o f a r c) = x (c i r c l e)

Insert known values =>

1.0 \times \frac{π}{1.08 \times 10^{4}} \times (r a d i a n) = x \times 2.0 \times π \times (r a d i a n)

Or

1.0 \cdot \frac{π}{1.08 \times 10^{4}} \cdot (r a d) = x \cdot 2.0 \times π \cdot (r a d)

Cancel SI units

1.0 \times \frac{π}{1.08 \times 10^{4}} \cdot (r a d) = x \times 2.0 \times π \times (r a d)

Conversion Equation

\frac{π}{1.08 \times 10^{4}} = x \times 2.0 \times π

Cancel factors on both sides

Cancel factors

\frac{π}{1.08 \times 10^{4}} = x \times π \times 2.0

Simplify

\frac{1.0}{1.08 \times 10^{4}} = x \times 2.0

Switch sides

x \times 2.0 = \frac{1.0}{1.08 \times 10^{4}}

Isolate

x

Multiply both sides by

(\frac{1.0}{2.0})

x \times 2.0 \times \frac{1.0}{2.0} = \frac{1.0}{1.08 \times 10^{4}} \times \frac{1.0}{2.0}

Cancel

x \times 2.0 \times \frac{1.0}{2.0} = \frac{1.0 \times 1.0}{1.08 \times 10^{4} \times 2.0}

Simplify

x = \frac{1.0}{1.08 \times 10^{4} \times 2.0}

Rewrite equation

\frac{1.0}{10^{4}} can be rewritten to 10^{- 4}

Rewrite

x = \frac{10^{- 4}}{1.08 \times 2.0}

Solve

x

x \approx 0.0000462963 \approx 4.6296 \times 10^{- 5}

Conversion Equation

1.0 (m i n u t e o f a r c) \approx 4.6296 \times 10^{- 5} (c i r c l e)

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