Convert pound / hour to tonne / second
Learn how to convert
1
pound / hour to
tonne / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{tonne}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{0.45359237}{3.6 \times 10^{3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{0.45359237}{3.6 \times 10^{3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{tonne}{second}\right) = {\color{rgb(125,164,120)} 907.18474\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)} = {\color{rgb(125,164,120)} 907.18474\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{tonne}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.45359237}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 907.18474}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.45359237}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 907.18474} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.45359237}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 907.18474} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{0.45359237}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times 907.18474\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 907.18474 = \dfrac{0.45359237}{3.6 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{907.18474}\right)\)
\({\color{rgb(20,165,174)} x} \times 907.18474 \times \dfrac{1.0}{907.18474} = \dfrac{0.45359237}{3.6 \times 10^{3}} \times \dfrac{1.0}{907.18474}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{907.18474}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{907.18474}}} = \dfrac{0.45359237 \times 1.0}{3.6 \times 10^{3} \times 907.18474}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.45359237}{3.6 \times 10^{3} \times 907.18474}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 0.45359237}{3.6 \times 907.18474}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000001389\approx1.3889 \times 10^{-7}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{hour}\right)\approx{\color{rgb(20,165,174)} 1.3889 \times 10^{-7}}\left(\dfrac{tonne}{second}\right)\)
