Convert inch / (minute • second) to inch / square hour
Learn how to convert
1
inch / (minute • second) to
inch / square hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{inch}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{square \text{ } hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{inch}{minute \times second}\right) = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{inch}{square \text{ } hour}\right) = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{inch}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{square \text{ } hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.54 \times 10^{-2}}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}}{1.296 \times 10^{7}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.296 \times 10^{7}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.296 \times 10^{7}} = \dfrac{1.0}{60.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.296 \times 10^{7}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.296 \times 10^{7}} \times \dfrac{1.296 \times 10^{7}}{1.0} = \dfrac{1.0}{60.0} \times \dfrac{1.296 \times 10^{7}}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{1.296}} \times {\color{rgb(166,218,227)} \cancel{10^{7}}}}{{\color{rgb(99,194,222)} \cancel{1.296}} \times {\color{rgb(166,218,227)} \cancel{10^{7}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 1.296 \times 10^{7}}{60.0 \times {\color{rgb(255,204,153)} \cancel{1.0}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.296 \times 10^{7}}{60.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 216000 = 2.16 \times 10^{5}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{inch}{minute \times second}\right) = {\color{rgb(20,165,174)} 2.16 \times 10^{5}}\left(\dfrac{inch}{square \text{ } hour}\right)\)
