Convert gram / (meter • hour) to gram / (meter • minute)
Learn how to convert
1
gram / (meter • hour) to
gram / (meter • minute)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{gram}{meter \times hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{meter \times minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(pascal \times second\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{gram}{meter \times hour}\right) = {\color{rgb(89,182,91)} \dfrac{2.5 \times 10^{-6}}{9.0}\left(pascal \times second\right)} = {\color{rgb(89,182,91)} \dfrac{2.5 \times 10^{-6}}{9.0}\left(Pa \cdot s\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{meter \times minute}\right) = {\color{rgb(125,164,120)} \dfrac{5.0 \times 10^{-5}}{3.0}\left(pascal \times second\right)} = {\color{rgb(125,164,120)} \dfrac{5.0 \times 10^{-5}}{3.0}\left(Pa \cdot s\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{gram}{meter \times hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{meter \times minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.5 \times 10^{-6}}{9.0}} \times {\color{rgb(89,182,91)} \left(pascal \times second\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{5.0 \times 10^{-5}}{3.0}}} \times {\color{rgb(125,164,120)} \left(pascal \times second\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.5 \times 10^{-6}}{9.0}} \cdot {\color{rgb(89,182,91)} \left(Pa \cdot s\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{5.0 \times 10^{-5}}{3.0}} \cdot {\color{rgb(125,164,120)} \left(Pa \cdot s\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.5 \times 10^{-6}}{9.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Pa \cdot s\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{5.0 \times 10^{-5}}{3.0}} \times {\color{rgb(125,164,120)} \cancel{\left(Pa \cdot s\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.5 \times 10^{-6}}{9.0} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0 \times 10^{-5}}{3.0}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{2.5 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-6}}}}{9.0} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0 \times {\color{rgb(255,204,153)} \cancel{10^{-5}}}}{3.0}\)
\(\text{Simplify}\)
\(\dfrac{2.5 \times 10^{-1}}{9.0} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{3.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{3.0} = \dfrac{2.5 \times 10^{-1}}{9.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.0}{5.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{3.0} \times \dfrac{3.0}{5.0} = \dfrac{2.5 \times 10^{-1}}{9.0} \times \dfrac{3.0}{5.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{5.0}} \times {\color{rgb(99,194,222)} \cancel{3.0}}}{{\color{rgb(99,194,222)} \cancel{3.0}} \times {\color{rgb(255,204,153)} \cancel{5.0}}} = \dfrac{2.5 \times 10^{-1} \times 3.0}{9.0 \times 5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.5 \times 10^{-1} \times 3.0}{9.0 \times 5.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0166666667\approx1.6667 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{gram}{meter \times hour}\right)\approx{\color{rgb(20,165,174)} 1.6667 \times 10^{-2}}\left(\dfrac{gram}{meter \times minute}\right)\)
