Convert kilogram / second to gram / hour
Learn how to convert
1
kilogram / second to
gram / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{gram}{second}\right) = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)} = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{10^{-3}}{3.6 \times 10^{3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}\)
Define the values of the selected prefixes
\(\text{Left side: } \dfrac{kilo}{1.0} = \dfrac{k}{1.0} = {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{-3}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{-3}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(250,175,0)} \dfrac{10^{3}}{1.0}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{-3}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-3} \times \dfrac{10^{3}}{1.0} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-3}}{3.6 \times 10^{3}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-3}}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-3}}{3.6 \times 10^{3}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-3}}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{10^{-3}} = 1.0 \times \dfrac{3.6 \times 10^{3}}{10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-3}}} \times {\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}} = 1.0 \times \dfrac{3.6 \times 10^{3}}{10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.6 \times 10^{3}}{10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{3} \times 3.6 \times 10^{3}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = 10^{6} \times 3.6\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 3600000 = 3.6 \times 10^{6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{second}\right) = {\color{rgb(20,165,174)} 3.6 \times 10^{6}}\left(\dfrac{gram}{hour}\right)\)
