Convert inch / minute to foot / second

Learn how to convert 1 inch / minute to foot / second step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(\dfrac{inch}{minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{foot}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{inch}{minute}\right) = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{meter}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}\left(\dfrac{m}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{foot}{second}\right) = {\color{rgb(125,164,120)} 3.048 \times 10^{-1}\left(\dfrac{meter}{second}\right)} = {\color{rgb(125,164,120)} 3.048 \times 10^{-1}\left(\dfrac{m}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{inch}{minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{foot}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.048 \times 10^{-1}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.048 \times 10^{-1}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.54 \times 10^{-2}}{60.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.048 \times 10^{-1}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.54 \times 10^{-2}}{60.0} = {\color{rgb(20,165,174)} x} \times 3.048 \times 10^{-1}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{2.54 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-2}}}}{60.0} = {\color{rgb(20,165,174)} x} \times 3.048 \times {\color{rgb(255,204,153)} \cancel{10^{-1}}}\)
\(\text{Simplify}\)
\(\dfrac{2.54 \times 10^{-1}}{60.0} = {\color{rgb(20,165,174)} x} \times 3.048\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.048 = \dfrac{2.54 \times 10^{-1}}{60.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.048}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.048 \times \dfrac{1.0}{3.048} = \dfrac{2.54 \times 10^{-1}}{60.0} \times \dfrac{1.0}{3.048}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.048}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.048}}} = \dfrac{2.54 \times 10^{-1} \times 1.0}{60.0 \times 3.048}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.54 \times 10^{-1}}{60.0 \times 3.048}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0013888889\approx1.3889 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{inch}{minute}\right)\approx{\color{rgb(20,165,174)} 1.3889 \times 10^{-3}}\left(\dfrac{foot}{second}\right)\)

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