Convert gram / (meter • second) to gram / (foot • hour)
Learn how to convert
1
gram / (meter • second) to
gram / (foot • hour)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{gram}{meter \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{foot \times hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(pascal \times second\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{gram}{meter \times second}\right) = {\color{rgb(89,182,91)} 10^{-3}\left(pascal \times second\right)} = {\color{rgb(89,182,91)} 10^{-3}\left(Pa \cdot s\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{gram}{foot \times hour}\right) = {\color{rgb(125,164,120)} 9.11344415281423 \times 10^{-7}\left(pascal \times second\right)} = {\color{rgb(125,164,120)} 9.11344415281423 \times 10^{-7}\left(Pa \cdot s\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{gram}{meter \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{foot \times hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left(pascal \times second\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 9.11344415281423 \times 10^{-7}}} \times {\color{rgb(125,164,120)} \left(pascal \times second\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(Pa \cdot s\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 9.11344415281423 \times 10^{-7}} \cdot {\color{rgb(125,164,120)} \left(Pa \cdot s\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Pa \cdot s\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 9.11344415281423 \times 10^{-7}} \times {\color{rgb(125,164,120)} \cancel{\left(Pa \cdot s\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-3} = {\color{rgb(20,165,174)} x} \times 9.11344415281423 \times 10^{-7}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times 9.11344415281423 \times {\color{rgb(255,204,153)} \cancelto{10^{-4}}{10^{-7}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 9.11344415281423 \times 10^{-4}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 9.11344415281423 \times 10^{-4} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{9.11344415281423 \times 10^{-4}}\right)\)
\({\color{rgb(20,165,174)} x} \times 9.11344415281423 \times 10^{-4} \times \dfrac{1.0}{9.11344415281423 \times 10^{-4}} = \times \dfrac{1.0}{9.11344415281423 \times 10^{-4}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{9.11344415281423}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{9.11344415281423}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}}} = \dfrac{1.0}{9.11344415281423 \times 10^{-4}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{9.11344415281423 \times 10^{-4}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-4}}\text{ can be rewritten to }10^{4}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{4}}{9.11344415281423}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1097.28\approx1.0973 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{gram}{meter \times second}\right)\approx{\color{rgb(20,165,174)} 1.0973 \times 10^{3}}\left(\dfrac{gram}{foot \times hour}\right)\)
