# Convert degree / (minute • second) to degree / (hour • second)

Learn how to convert 1 degree / (minute • second) to degree / (hour • second) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{degree}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{hour \times second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{degree}{minute \times second}\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{degree}{hour \times second}\right) = {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{degree}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{hour \times second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{1.08 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{7.2 \times 10^{4}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{1.08 \times {\color{rgb(99,194,222)} \cancel{10^{4}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{7.2 \times {\color{rgb(99,194,222)} \cancel{10^{4}}}}$$
$$\text{Simplify}$$
$$\dfrac{1.0}{1.08} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{7.2}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{7.2} = \dfrac{1.0}{1.08}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{7.2}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{7.2} \times \dfrac{7.2}{1.0} = \dfrac{1.0}{1.08} \times \dfrac{7.2}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{7.2}}}{{\color{rgb(99,194,222)} \cancel{7.2}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 7.2}{1.08 \times {\color{rgb(255,204,153)} \cancel{1.0}}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{7.2}{1.08}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx6.6666666667\approx6.6667$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{degree}{minute \times second}\right)\approx{\color{rgb(20,165,174)} 6.6667}\left(\dfrac{degree}{hour \times second}\right)$$