Convert bu(分) to fermi
Learn how to convert
1
bu(分) to
fermi
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(bu(分)\right)={\color{rgb(20,165,174)} x}\left(fermi\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(bu(分)\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{3.3 \times 10^{2}}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{3.3 \times 10^{2}}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(fermi\right) = {\color{rgb(125,164,120)} 10^{-15}\left(meter\right)} = {\color{rgb(125,164,120)} 10^{-15}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(bu(分)\right)={\color{rgb(20,165,174)} x}\left(fermi\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.3 \times 10^{2}}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-15}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{3.3 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-15}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.3 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-15}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{3.3 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times 10^{-15}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-15} = \dfrac{1.0}{3.3 \times 10^{2}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-15}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-15} \times \dfrac{1.0}{10^{-15}} = \dfrac{1.0}{3.3 \times 10^{2}} \times \dfrac{1.0}{10^{-15}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-15}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-15}}}} = \dfrac{1.0 \times 1.0}{3.3 \times {\color{rgb(255,204,153)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancelto{10^{-13}}{10^{-15}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{3.3 \times 10^{-13}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-13}}\text{ can be rewritten to }10^{13}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{13}}{3.3}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx3.0303030303 \times 10^{12}\approx3.0303 \times 10^{12}\)
\(\text{Conversion Equation}\)
\(1.0\left(bu(分)\right)\approx{\color{rgb(20,165,174)} 3.0303 \times 10^{12}}\left(fermi\right)\)
