Convert angular mil to second of arc

Learn how to convert 1 angular mil to second of arc step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(angular \text{ } mil\right)={\color{rgb(20,165,174)} x}\left(second \text{ } of \text{ } arc\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)
\(\text{Left side: 1.0 } \left(angular \text{ } mil\right) = {\color{rgb(89,182,91)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}\left(radian\right)} = {\color{rgb(89,182,91)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}\left(rad\right)}\)
\(\text{Right side: 1.0 } \left(second \text{ } of \text{ } arc\right) = {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}\left(radian\right)} = {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}\left(rad\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(angular \text{ } mil\right)={\color{rgb(20,165,174)} x}\left(second \text{ } of \text{ } arc\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times \dfrac{π}{6.4 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)
\(\text{Conversion Equation}\)
\(2.0 \times \dfrac{π}{6.4 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{6.48 \times 10^{5}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times 2.0}{6.4 \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{6.48 \times {\color{rgb(99,194,222)} \cancelto{10^{2}}{10^{5}}}}\)
\(\dfrac{2.0}{6.4} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{6.48 \times 10^{2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{6.48 \times 10^{2}} = \dfrac{2.0}{6.4}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{6.48 \times 10^{2}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{6.48 \times 10^{2}} \times \dfrac{6.48 \times 10^{2}}{1.0} = \dfrac{2.0}{6.4} \times \dfrac{6.48 \times 10^{2}}{1.0}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{6.48}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}}}{{\color{rgb(99,194,222)} \cancel{6.48}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{2.0 \times 6.48 \times 10^{2}}{6.4 \times 1.0}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.0 \times 6.48 \times 10^{2}}{6.4}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 202.5 = 2.025 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(angular \text{ } mil\right) = {\color{rgb(20,165,174)} 2.025 \times 10^{2}}\left(second \text{ } of \text{ } arc\right)\)

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