Convert inch / (minute • second) to gal
Learn how to convert
1
inch / (minute • second) to
gal
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{inch}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(gal\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{inch}{minute \times second}\right) = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(gal\right) = {\color{rgb(125,164,120)} 10^{-2}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 10^{-2}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{inch}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(gal\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-2}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-2}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.54 \times 10^{-2}}{60.0} = {\color{rgb(20,165,174)} x} \times 10^{-2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{2.54 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}}{60.0} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}\)
\(\text{Simplify}\)
\(\dfrac{2.54}{60.0} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = \dfrac{2.54}{60.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0423333333\approx4.2333 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{inch}{minute \times second}\right)\approx{\color{rgb(20,165,174)} 4.2333 \times 10^{-2}}\left(gal\right)\)
