# Convert parsec to fall

Learn how to convert 1 parsec to fall step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(parsec\right)={\color{rgb(20,165,174)} x}\left(fall\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(meter\right)$$
$$\text{Left side: 1.0 } \left(parsec\right) = {\color{rgb(89,182,91)} 3.08567400801506 \times 10^{16}\left(meter\right)} = {\color{rgb(89,182,91)} 3.08567400801506 \times 10^{16}\left(m\right)}$$
$$\text{Right side: 1.0 } \left(fall\right) = {\color{rgb(125,164,120)} 5.67\left(meter\right)} = {\color{rgb(125,164,120)} 5.67\left(m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(parsec\right)={\color{rgb(20,165,174)} x}\left(fall\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 3.08567400801506 \times 10^{16}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 5.67}} \times {\color{rgb(125,164,120)} \left(meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 3.08567400801506 \times 10^{16}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 5.67} \cdot {\color{rgb(125,164,120)} \left(m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 3.08567400801506 \times 10^{16}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 5.67} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}$$
$$\text{Conversion Equation}$$
$$3.08567400801506 \times 10^{16} = {\color{rgb(20,165,174)} x} \times 5.67$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 5.67 = 3.08567400801506 \times 10^{16}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{5.67}\right)$$
$${\color{rgb(20,165,174)} x} \times 5.67 \times \dfrac{1.0}{5.67} = 3.08567400801506 \times 10^{16} \times \dfrac{1.0}{5.67}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{5.67}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{5.67}}} = 3.08567400801506 \times 10^{16} \times \dfrac{1.0}{5.67}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{3.08567400801506 \times 10^{16}}{5.67}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx5.4421058342 \times 10^{15}\approx5.4421 \times 10^{15}$$
$$\text{Conversion Equation}$$
$$1.0\left(parsec\right)\approx{\color{rgb(20,165,174)} 5.4421 \times 10^{15}}\left(fall\right)$$