Convert inch / minute to mach
Learn how to convert
1
inch / minute to
mach
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{inch}{minute}\right)={\color{rgb(20,165,174)} x}\left(mach\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{inch}{minute}\right) = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{meter}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{m}{s}\right)}\)
\(\text{Right side: 1.0 } \left(mach\right) = {\color{rgb(125,164,120)} 331.0\left(\dfrac{meter}{second}\right)} = {\color{rgb(125,164,120)} 331.0\left(\dfrac{m}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{inch}{minute}\right)={\color{rgb(20,165,174)} x}\left(mach\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 331.0}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 331.0} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 331.0} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.54 \times 10^{-2}}{60.0} = {\color{rgb(20,165,174)} x} \times 331.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 331.0 = \dfrac{2.54 \times 10^{-2}}{60.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{331.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 331.0 \times \dfrac{1.0}{331.0} = \dfrac{2.54 \times 10^{-2}}{60.0} \times \dfrac{1.0}{331.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{331.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{331.0}}} = \dfrac{2.54 \times 10^{-2} \times 1.0}{60.0 \times 331.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.54 \times 10^{-2}}{60.0 \times 331.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.000001279\approx1.279 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{inch}{minute}\right)\approx{\color{rgb(20,165,174)} 1.279 \times 10^{-6}}\left(mach\right)\)
