Convert decade to lustrum
Learn how to convert
1
decade to
lustrum
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(decade\right)={\color{rgb(20,165,174)} x}\left(lustrum\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(second\right)\)
\(\text{Left side: 1.0 } \left(decade\right) = {\color{rgb(89,182,91)} 3.1536 \times 10^{8}\left(second\right)} = {\color{rgb(89,182,91)} 3.1536 \times 10^{8}\left(s\right)}\)
\(\text{Right side: 1.0 } \left(lustrum\right) = {\color{rgb(125,164,120)} 1.5768 \times 10^{8}\left(second\right)} = {\color{rgb(125,164,120)} 1.5768 \times 10^{8}\left(s\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(decade\right)={\color{rgb(20,165,174)} x}\left(lustrum\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 3.1536 \times 10^{8}} \times {\color{rgb(89,182,91)} \left(second\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.5768 \times 10^{8}}} \times {\color{rgb(125,164,120)} \left(second\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 3.1536 \times 10^{8}} \cdot {\color{rgb(89,182,91)} \left(s\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.5768 \times 10^{8}} \cdot {\color{rgb(125,164,120)} \left(s\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 3.1536 \times 10^{8}} \cdot {\color{rgb(89,182,91)} \cancel{\left(s\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.5768 \times 10^{8}} \times {\color{rgb(125,164,120)} \cancel{\left(s\right)}}\)
\(\text{Conversion Equation}\)
\(3.1536 \times 10^{8} = {\color{rgb(20,165,174)} x} \times 1.5768 \times 10^{8}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(3.1536 \times {\color{rgb(255,204,153)} \cancel{10^{8}}} = {\color{rgb(20,165,174)} x} \times 1.5768 \times {\color{rgb(255,204,153)} \cancel{10^{8}}}\)
\(\text{Simplify}\)
\(3.1536 = {\color{rgb(20,165,174)} x} \times 1.5768\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.5768 = 3.1536\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.5768}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.5768 \times \dfrac{1.0}{1.5768} = 3.1536 \times \dfrac{1.0}{1.5768}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.5768}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.5768}}} = 3.1536 \times \dfrac{1.0}{1.5768}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.1536}{1.5768}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 2\)
\(\text{Conversion Equation}\)
\(1.0\left(decade\right) = {\color{rgb(20,165,174)} 2}\left(lustrum\right)\)
