# Convert minute of arc to half circle

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

## Calculation Breakdown

Set up the equation
$$1.0\left(minute \text{ } of \text{ } arc\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(radian\right)$$
$$\text{Left side: 1.0 } \left(minute \text{ } of \text{ } arc\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}\left(rad\right)}$$
$$\text{Right side: 1.0 } \left(half \text{ } circle\right) = {\color{rgb(125,164,120)} π\left(radian\right)} = {\color{rgb(125,164,120)} π\left(rad\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(minute \text{ } of \text{ } arc\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} π}} \times {\color{rgb(125,164,120)} \left(radian\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} π} \cdot {\color{rgb(125,164,120)} \left(rad\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} π} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times π$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}}$$
$$\text{Simplify}$$
$$\dfrac{1.0}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x}$$
Switch sides
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.08 \times 10^{4}}$$
Rewrite equation
$$\dfrac{1.0}{10^{4}}\text{ can be rewritten to }10^{-4}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-4}}{1.08}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000925926\approx9.2593 \times 10^{-5}$$
$$\text{Conversion Equation}$$
$$1.0\left(minute \text{ } of \text{ } arc\right)\approx{\color{rgb(20,165,174)} 9.2593 \times 10^{-5}}\left(half \text{ } circle\right)$$