Convert lucsec to erg / second
Learn how to convert
1
lucsec to
erg / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(lucsec\right)={\color{rgb(20,165,174)} x}\left(\dfrac{erg}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(watt\right)\)
\(\text{Left side: 1.0 } \left(lucsec\right) = {\color{rgb(89,182,91)} 1.33322387415 \times 10^{-4}\left(watt\right)} = {\color{rgb(89,182,91)} 1.33322387415 \times 10^{-4}\left(W\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{erg}{second}\right) = {\color{rgb(125,164,120)} 10^{-7}\left(watt\right)} = {\color{rgb(125,164,120)} 10^{-7}\left(W\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(lucsec\right)={\color{rgb(20,165,174)} x}\left(\dfrac{erg}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.33322387415 \times 10^{-4}} \times {\color{rgb(89,182,91)} \left(watt\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-7}}} \times {\color{rgb(125,164,120)} \left(watt\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.33322387415 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(W\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-7}} \cdot {\color{rgb(125,164,120)} \left(W\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.33322387415 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(W\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-7}} \times {\color{rgb(125,164,120)} \cancel{\left(W\right)}}\)
\(\text{Conversion Equation}\)
\(1.33322387415 \times 10^{-4} = {\color{rgb(20,165,174)} x} \times 10^{-7}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(1.33322387415 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{-3}}{10^{-7}}}\)
\(\text{Simplify}\)
\(1.33322387415 = {\color{rgb(20,165,174)} x} \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-3} = 1.33322387415\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-3} \times \dfrac{1.0}{10^{-3}} = 1.33322387415 \times \dfrac{1.0}{10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-3}}}} = 1.33322387415 \times \dfrac{1.0}{10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.33322387415}{10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{3} \times 1.33322387415\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1333.2238742\approx1.3332 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(lucsec\right)\approx{\color{rgb(20,165,174)} 1.3332 \times 10^{3}}\left(\dfrac{erg}{second}\right)\)
