Convert hao(毫) to inch
Learn how to convert
1
hao(毫) to
inch
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(hao(毫)\right)={\color{rgb(20,165,174)} x}\left(inch\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(hao(毫)\right) = {\color{rgb(89,182,91)} 10^{-4}\left(meter\right)} = {\color{rgb(89,182,91)} 10^{-4}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(inch\right) = {\color{rgb(125,164,120)} 2.54 \times 10^{-2}\left(meter\right)} = {\color{rgb(125,164,120)} 2.54 \times 10^{-2}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(hao(毫)\right)={\color{rgb(20,165,174)} x}\left(inch\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-4}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.54 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.54 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.54 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-4} = {\color{rgb(20,165,174)} x} \times 2.54 \times 10^{-2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-4}}} = {\color{rgb(20,165,174)} x} \times 2.54 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}\)
\(\text{Simplify}\)
\(10^{-2} = {\color{rgb(20,165,174)} x} \times 2.54\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.54 = 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.54}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.54 \times \dfrac{1.0}{2.54} = 10^{-2} \times \dfrac{1.0}{2.54}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.54}}} = 10^{-2} \times \dfrac{1.0}{2.54}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2}}{2.54}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0039370079\approx3.937 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(hao(毫)\right)\approx{\color{rgb(20,165,174)} 3.937 \times 10^{-3}}\left(inch\right)\)
