Convert parsec to astronomical unit

Learn how to convert 1 parsec to astronomical unit step by step.

Calculation Breakdown

Set up the equation

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

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

(m e t e r)

Left side: 1.0 (p a r s e c) = 3.08567400801506 \times 10^{16} (m e t e r) = 3.08567400801506 \times 10^{16} (m)

Right side: 1.0 (a s t r o n o m i c a l u n i t) = 149597870691.0 (m e t e r) = 149597870691.0 (m)

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times 3.08567400801506 \times 10^{16} \times (m e t e r) = x \times 149597870691.0 \times (m e t e r)

Or

1.0 \cdot 3.08567400801506 \times 10^{16} \cdot (m) = x \cdot 149597870691.0 \cdot (m)

Cancel SI units

1.0 \times 3.08567400801506 \times 10^{16} \cdot (m) = x \times 149597870691.0 \times (m)

Conversion Equation

3.08567400801506 \times 10^{16} = x \times 149597870691.0

Switch sides

x \times 149597870691.0 = 3.08567400801506 \times 10^{16}

Isolate

x

Multiply both sides by

(\frac{1.0}{149597870691.0})

x \times 149597870691.0 \times \frac{1.0}{149597870691.0} = 3.08567400801506 \times 10^{16} \times \frac{1.0}{149597870691.0}

Cancel

x \times 149597870691.0 \times \frac{1.0}{149597870691.0} = 3.08567400801506 \times 10^{16} \times \frac{1.0}{149597870691.0}

Simplify

x = \frac{3.08567400801506 \times 10^{16}}{149597870691.0}

Solve

x

x \approx 206264.56739 \approx 2.0626 \times 10^{5}

Conversion Equation

1.0 (p a r s e c) \approx 2.0626 \times 10^{5} (a s t r o n o m i c a l u n i t)

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