Convert cubic meter of atmosphere to quad
Learn how to convert
1
cubic meter of atmosphere to
quad
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right)={\color{rgb(20,165,174)} x}\left(quad\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right) = {\color{rgb(89,182,91)} 1.01325 \times 10^{-4}\left(joule\right)} = {\color{rgb(89,182,91)} 1.01325 \times 10^{-4}\left(J\right)}\)
\(\text{Right side: 1.0 } \left(quad\right) = {\color{rgb(125,164,120)} 1.05435026444 \times 10^{18}\left(joule\right)} = {\color{rgb(125,164,120)} 1.05435026444 \times 10^{18}\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right)={\color{rgb(20,165,174)} x}\left(quad\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.01325 \times 10^{-4}} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.05435026444 \times 10^{18}}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.01325 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.05435026444 \times 10^{18}} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.01325 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.05435026444 \times 10^{18}} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(1.01325 \times 10^{-4} = {\color{rgb(20,165,174)} x} \times 1.05435026444 \times 10^{18}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.05435026444 \times 10^{18} = 1.01325 \times 10^{-4}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.05435026444 \times 10^{18}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.05435026444 \times 10^{18} \times \dfrac{1.0}{1.05435026444 \times 10^{18}} = 1.01325 \times 10^{-4} \times \dfrac{1.0}{1.05435026444 \times 10^{18}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.05435026444}} \times {\color{rgb(99,194,222)} \cancel{10^{18}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.05435026444}} \times {\color{rgb(99,194,222)} \cancel{10^{18}}}} = 1.01325 \times 10^{-4} \times \dfrac{1.0}{1.05435026444 \times 10^{18}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.01325 \times 10^{-4}}{1.05435026444 \times 10^{18}}\)
Rewrite equation
\(\dfrac{1.0}{10^{18}}\text{ can be rewritten to }10^{-18}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-18} \times 1.01325 \times 10^{-4}}{1.05435026444}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-22} \times 1.01325}{1.05435026444}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx9.6101839604 \times 10^{-23}\approx9.6102 \times 10^{-23}\)
\(\text{Conversion Equation}\)
\(1.0\left(cubic \text{ } meter \text{ } of \text{ } atmosphere\right)\approx{\color{rgb(20,165,174)} 9.6102 \times 10^{-23}}\left(quad\right)\)
