Convert pascal to atmosphere
Learn how to convert
1
pascal to
atmosphere
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(pascal\right)={\color{rgb(20,165,174)} x}\left(atmosphere\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(pascal\right)\)
\(\text{Left side: 1.0 } \left(pascal\right) = {\color{rgb(89,182,91)} 1.0\left(pascal\right)} = {\color{rgb(89,182,91)} 1.0\left(Pa\right)}\)
\(\text{Right side: 1.0 } \left(atmosphere\right) = {\color{rgb(125,164,120)} 1.01325 \times 10^{5}\left(pascal\right)} = {\color{rgb(125,164,120)} 1.01325 \times 10^{5}\left(Pa\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(pascal\right)={\color{rgb(20,165,174)} x}\left(atmosphere\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(pascal\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.01325 \times 10^{5}}} \times {\color{rgb(125,164,120)} \left(pascal\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(Pa\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.01325 \times 10^{5}} \cdot {\color{rgb(125,164,120)} \left(Pa\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(Pa\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.01325 \times 10^{5}} \times {\color{rgb(125,164,120)} \cancel{\left(Pa\right)}}\)
\(\text{Conversion Equation}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 1.01325 \times 10^{5}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 1.01325 \times 10^{5}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.01325 \times 10^{5} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.01325 \times 10^{5}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.01325 \times 10^{5} \times \dfrac{1.0}{1.01325 \times 10^{5}} = 1.0 \times \dfrac{1.0}{1.01325 \times 10^{5}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.01325}} \times {\color{rgb(99,194,222)} \cancel{10^{5}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.01325}} \times {\color{rgb(99,194,222)} \cancel{10^{5}}}} = 1.0 \times \dfrac{1.0}{1.01325 \times 10^{5}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.01325 \times 10^{5}}\)
Rewrite equation
\(\dfrac{1.0}{10^{5}}\text{ can be rewritten to }10^{-5}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-5}}{1.01325}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000098692\approx9.8692 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(pascal\right)\approx{\color{rgb(20,165,174)} 9.8692 \times 10^{-6}}\left(atmosphere\right)\)
