Convert pond to sthene
Learn how to convert
1
pond to
sthene
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(pond\right)={\color{rgb(20,165,174)} x}\left(sthene\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton\right)\)
\(\text{Left side: 1.0 } \left(pond\right) = {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}\left(newton\right)} = {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}\left(N\right)}\)
\(\text{Right side: 1.0 } \left(sthene\right) = {\color{rgb(125,164,120)} 10^{3}\left(newton\right)} = {\color{rgb(125,164,120)} 10^{3}\left(N\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(pond\right)={\color{rgb(20,165,174)} x}\left(sthene\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left(newton\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{3}}} \times {\color{rgb(125,164,120)} \left(newton\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(N\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{3}} \cdot {\color{rgb(125,164,120)} \left(N\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(N\right)}}\)
\(\text{Conversion Equation}\)
\(9.80665 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 10^{3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{3} = 9.80665 \times 10^{-3}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{3} \times \dfrac{1.0}{10^{3}} = 9.80665 \times 10^{-3} \times \dfrac{1.0}{10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{3}}}} = 9.80665 \times 10^{-3} \times \dfrac{1.0}{10^{3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{9.80665 \times 10^{-3}}{10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{-3} \times 9.80665 \times 10^{-3}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = 10^{-6} \times 9.80665\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 9.80665 \times 10^{-6}\approx9.8066 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(pond\right)\approx{\color{rgb(20,165,174)} 9.8066 \times 10^{-6}}\left(sthene\right)\)
