Convert shaku(尺) to marathon
Learn how to convert
1
shaku(尺) to
marathon
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(shaku(尺)\right)={\color{rgb(20,165,174)} x}\left(marathon\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(shaku(尺)\right) = {\color{rgb(89,182,91)} \dfrac{10.0}{33.0}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{10.0}{33.0}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(marathon\right) = {\color{rgb(125,164,120)} 3.675 \times 10^{4}\left(meter\right)} = {\color{rgb(125,164,120)} 3.675 \times 10^{4}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(shaku(尺)\right)={\color{rgb(20,165,174)} x}\left(marathon\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10.0}{33.0}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.675 \times 10^{4}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10.0}{33.0}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.675 \times 10^{4}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10.0}{33.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.675 \times 10^{4}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10.0}{33.0} = {\color{rgb(20,165,174)} x} \times 3.675 \times 10^{4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{10.0}}}{33.0} = {\color{rgb(20,165,174)} x} \times 3.675 \times {\color{rgb(255,204,153)} \cancelto{10^{3}}{10^{4}}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.675 \times 10^{3} = \dfrac{1.0}{33.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.675 \times 10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.675 \times 10^{3} \times \dfrac{1.0}{3.675 \times 10^{3}} = \dfrac{1.0}{33.0} \times \dfrac{1.0}{3.675 \times 10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.675}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.675}} \times {\color{rgb(99,194,222)} \cancel{10^{3}}}} = \dfrac{1.0 \times 1.0}{33.0 \times 3.675 \times 10^{3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{33.0 \times 3.675 \times 10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3}}{33.0 \times 3.675}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000082457\approx8.2457 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(shaku(尺)\right)\approx{\color{rgb(20,165,174)} 8.2457 \times 10^{-6}}\left(marathon\right)\)
