Convert meter / square hour to inch / (minute • second)
Learn how to convert
1
meter / square hour to
inch / (minute • second)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{meter}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{minute \times second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{meter}{square \text{ } hour}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{inch}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{meter}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{minute \times second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{1.296 \times 10^{7}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{60.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{60.0} = \dfrac{1.0}{1.296 \times 10^{7}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{60.0}{2.54 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{60.0} \times \dfrac{60.0}{2.54 \times 10^{-2}} = \dfrac{1.0}{1.296 \times 10^{7}} \times \dfrac{60.0}{2.54 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{60.0}}}{{\color{rgb(166,218,227)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = \dfrac{1.0 \times 60.0}{1.296 \times {\color{rgb(255,204,153)} \cancelto{10^{5}}{10^{7}}} \times 2.54 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{60.0}{1.296 \times 10^{5} \times 2.54}\)
Rewrite equation
\(\dfrac{1.0}{10^{5}}\text{ can be rewritten to }10^{-5}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-5} \times 60.0}{1.296 \times 2.54}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0001822689\approx1.8227 \times 10^{-4}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{meter}{square \text{ } hour}\right)\approx{\color{rgb(20,165,174)} 1.8227 \times 10^{-4}}\left(\dfrac{inch}{minute \times second}\right)\)
