Convert lustrum to quarter
Learn how to convert
1
lustrum to
quarter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(lustrum\right)={\color{rgb(20,165,174)} x}\left(quarter\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(second\right)\)
\(\text{Left side: 1.0 } \left(lustrum\right) = {\color{rgb(89,182,91)} 1.5768 \times 10^{8}\left(second\right)} = {\color{rgb(89,182,91)} 1.5768 \times 10^{8}\left(s\right)}\)
\(\text{Right side: 1.0 } \left(quarter\right) = {\color{rgb(125,164,120)} 7.776 \times 10^{6}\left(second\right)} = {\color{rgb(125,164,120)} 7.776 \times 10^{6}\left(s\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(lustrum\right)={\color{rgb(20,165,174)} x}\left(quarter\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.5768 \times 10^{8}} \times {\color{rgb(89,182,91)} \left(second\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 7.776 \times 10^{6}}} \times {\color{rgb(125,164,120)} \left(second\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.5768 \times 10^{8}} \cdot {\color{rgb(89,182,91)} \left(s\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 7.776 \times 10^{6}} \cdot {\color{rgb(125,164,120)} \left(s\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.5768 \times 10^{8}} \cdot {\color{rgb(89,182,91)} \cancel{\left(s\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 7.776 \times 10^{6}} \times {\color{rgb(125,164,120)} \cancel{\left(s\right)}}\)
\(\text{Conversion Equation}\)
\(1.5768 \times 10^{8} = {\color{rgb(20,165,174)} x} \times 7.776 \times 10^{6}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(1.5768 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{8}}} = {\color{rgb(20,165,174)} x} \times 7.776 \times {\color{rgb(255,204,153)} \cancel{10^{6}}}\)
\(\text{Simplify}\)
\(1.5768 \times 10^{2} = {\color{rgb(20,165,174)} x} \times 7.776\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 7.776 = 1.5768 \times 10^{2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{7.776}\right)\)
\({\color{rgb(20,165,174)} x} \times 7.776 \times \dfrac{1.0}{7.776} = 1.5768 \times 10^{2} \times \dfrac{1.0}{7.776}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{7.776}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{7.776}}} = 1.5768 \times 10^{2} \times \dfrac{1.0}{7.776}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.5768 \times 10^{2}}{7.776}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx20.277777778\approx20.2778\)
\(\text{Conversion Equation}\)
\(1.0\left(lustrum\right)\approx{\color{rgb(20,165,174)} 20.2778}\left(quarter\right)\)
