Convert mile / square second to galileo
Learn how to convert
1
mile / square second to
galileo
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mile}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(galileo\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mile}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(galileo\right) = {\color{rgb(125,164,120)} 10^{-2}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 10^{-2}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mile}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(galileo\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1609.344} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-2}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-2}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(1609.344 = {\color{rgb(20,165,174)} x} \times 10^{-2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-2} = 1609.344\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-2} \times \dfrac{1.0}{10^{-2}} = 1609.344 \times \dfrac{1.0}{10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-2}}}} = 1609.344 \times \dfrac{1.0}{10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1609.344}{10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{2} \times 1609.344\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 160934.4\approx1.6093 \times 10^{5}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mile}{square \text{ } second}\right)\approx{\color{rgb(20,165,174)} 1.6093 \times 10^{5}}\left(galileo\right)\)
