Convert si(丝) to mile
Learn how to convert
1
si(丝) to
mile
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(si(丝)\right)={\color{rgb(20,165,174)} x}\left(mile\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(si(丝)\right) = {\color{rgb(89,182,91)} 10^{-5}\left(meter\right)} = {\color{rgb(89,182,91)} 10^{-5}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(mile\right) = {\color{rgb(125,164,120)} 1807.3116\left(meter\right)} = {\color{rgb(125,164,120)} 1807.3116\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(si(丝)\right)={\color{rgb(20,165,174)} x}\left(mile\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1807.3116}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1807.3116} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1807.3116} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-5} = {\color{rgb(20,165,174)} x} \times 1807.3116\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1807.3116 = 10^{-5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1807.3116}\right)\)
\({\color{rgb(20,165,174)} x} \times 1807.3116 \times \dfrac{1.0}{1807.3116} = 10^{-5} \times \dfrac{1.0}{1807.3116}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1807.3116}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1807.3116}}} = 10^{-5} \times \dfrac{1.0}{1807.3116}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-5}}{1807.3116}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000000055\approx5.5331 \times 10^{-9}\)
\(\text{Conversion Equation}\)
\(1.0\left(si(丝)\right)\approx{\color{rgb(20,165,174)} 5.5331 \times 10^{-9}}\left(mile\right)\)
