Convert acre • inch to gallon
Learn how to convert
1
acre • inch to
gallon
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(acre \times inch\right)={\color{rgb(20,165,174)} x}\left(gallon\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(acre \times inch\right) = {\color{rgb(89,182,91)} 102.79015312896\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 102.79015312896\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(gallon\right) = {\color{rgb(125,164,120)} 3.785411784 \times 10^{-3}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 3.785411784 \times 10^{-3}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(acre \times inch\right)={\color{rgb(20,165,174)} x}\left(gallon\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 102.79015312896} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.785411784 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 102.79015312896} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.785411784 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 102.79015312896} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.785411784 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(102.79015312896 = {\color{rgb(20,165,174)} x} \times 3.785411784 \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.785411784 \times 10^{-3} = 102.79015312896\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.785411784 \times 10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.785411784 \times 10^{-3} \times \dfrac{1.0}{3.785411784 \times 10^{-3}} = 102.79015312896 \times \dfrac{1.0}{3.785411784 \times 10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.785411784}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.785411784}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = 102.79015312896 \times \dfrac{1.0}{3.785411784 \times 10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{102.79015312896}{3.785411784 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 102.79015312896}{3.785411784}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx27154.285714\approx2.7154 \times 10^{4}\)
\(\text{Conversion Equation}\)
\(1.0\left(acre \times inch\right)\approx{\color{rgb(20,165,174)} 2.7154 \times 10^{4}}\left(gallon\right)\)
