Convert mile / square second to inch / (hour • second)

Learn how to convert 1 mile / square second to inch / (hour • second) step by step.

Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{mile}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{hour \times second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{meter}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{mile}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{m}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{inch}{hour \times second}\right) = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{mile}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{hour \times second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1609.344} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$1609.344 = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}} = 1609.344$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{3.6 \times 10^{3}}{2.54 \times 10^{-2}}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{2.54 \times 10^{-2}} = 1609.344 \times \dfrac{3.6 \times 10^{3}}{2.54 \times 10^{-2}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{3.6}} \times {\color{rgb(76,153,0)} \cancel{10^{3}}}}{{\color{rgb(166,218,227)} \cancel{3.6}} \times {\color{rgb(76,153,0)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = 1609.344 \times \dfrac{3.6 \times 10^{3}}{2.54 \times 10^{-2}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1609.344 \times 3.6 \times 10^{3}}{2.54 \times 10^{-2}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 1609.344 \times 3.6 \times 10^{3}}{2.54}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 1609.344 \times 3.6}{2.54}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 228096000\approx2.281 \times 10^{8}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{mile}{square \text{ } second}\right)\approx{\color{rgb(20,165,174)} 2.281 \times 10^{8}}\left(\dfrac{inch}{hour \times second}\right)$$