Convert inch / (hour • minute) to inch / square minute
Learn how to convert
1
inch / (hour • minute) to
inch / square minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{inch}{hour \times minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{square \text{ } minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{inch}{hour \times minute}\right) = {\color{rgb(89,182,91)} \dfrac{0.0254}{2.16 \times 10^{5}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{0.0254}{2.16 \times 10^{5}}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{inch}{square \text{ } minute}\right) = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{inch}{hour \times minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{square \text{ } minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.0254}{2.16 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.0254}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.0254}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{0.0254}{2.16 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{0.0254}{2.16 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}\)
\(\text{Simplify}\)
\(\dfrac{0.0254}{2.16 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6} = \dfrac{0.0254}{2.16 \times 10^{2}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6}{2.54 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{3.6} \times \dfrac{3.6}{2.54 \times 10^{-2}} = \dfrac{0.0254}{2.16 \times 10^{2}} \times \dfrac{3.6}{2.54 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{3.6}}}{{\color{rgb(166,218,227)} \cancel{3.6}} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = \dfrac{0.0254 \times 3.6}{2.16 \times {\color{rgb(255,204,153)} \cancel{10^{2}}} \times 2.54 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.0254 \times 3.6}{2.16 \times 2.54}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0166666667\approx1.6667 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{inch}{hour \times minute}\right)\approx{\color{rgb(20,165,174)} 1.6667 \times 10^{-2}}\left(\dfrac{inch}{square \text{ } minute}\right)\)
