Convert gal to mile / square second
Learn how to convert
1
gal to
mile / square second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gal\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(gal\right) = {\color{rgb(89,182,91)} 10^{-2}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 10^{-2}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{mile}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 1609.344\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 1609.344\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gal\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-2}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1609.344}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-2}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1609.344} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1609.344} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-2} = {\color{rgb(20,165,174)} x} \times 1609.344\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1609.344 = 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1609.344}\right)\)
\({\color{rgb(20,165,174)} x} \times 1609.344 \times \dfrac{1.0}{1609.344} = 10^{-2} \times \dfrac{1.0}{1609.344}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1609.344}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1609.344}}} = 10^{-2} \times \dfrac{1.0}{1609.344}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2}}{1609.344}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000062137\approx6.2137 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(gal\right)\approx{\color{rgb(20,165,174)} 6.2137 \times 10^{-6}}\left(\dfrac{mile}{square \text{ } second}\right)\)
