Convert year to decade
Learn how to convert
1
year to
decade
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(year\right)={\color{rgb(20,165,174)} x}\left(decade\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(second\right)\)
\(\text{Left side: 1.0 } \left(year\right) = {\color{rgb(89,182,91)} 31299264.0\left(second\right)} = {\color{rgb(89,182,91)} 31299264.0\left(s\right)}\)
\(\text{Right side: 1.0 } \left(decade\right) = {\color{rgb(125,164,120)} 3.1536 \times 10^{8}\left(second\right)} = {\color{rgb(125,164,120)} 3.1536 \times 10^{8}\left(s\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(year\right)={\color{rgb(20,165,174)} x}\left(decade\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 31299264.0} \times {\color{rgb(89,182,91)} \left(second\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.1536 \times 10^{8}}} \times {\color{rgb(125,164,120)} \left(second\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 31299264.0} \cdot {\color{rgb(89,182,91)} \left(s\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.1536 \times 10^{8}} \cdot {\color{rgb(125,164,120)} \left(s\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 31299264.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(s\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.1536 \times 10^{8}} \times {\color{rgb(125,164,120)} \cancel{\left(s\right)}}\)
\(\text{Conversion Equation}\)
\(31299264.0 = {\color{rgb(20,165,174)} x} \times 3.1536 \times 10^{8}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.1536 \times 10^{8} = 31299264.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.1536 \times 10^{8}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.1536 \times 10^{8} \times \dfrac{1.0}{3.1536 \times 10^{8}} = 31299264.0 \times \dfrac{1.0}{3.1536 \times 10^{8}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.1536}} \times {\color{rgb(99,194,222)} \cancel{10^{8}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.1536}} \times {\color{rgb(99,194,222)} \cancel{10^{8}}}} = 31299264.0 \times \dfrac{1.0}{3.1536 \times 10^{8}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{31299264.0}{3.1536 \times 10^{8}}\)
Rewrite equation
\(\dfrac{1.0}{10^{8}}\text{ can be rewritten to }10^{-8}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-8} \times 31299264.0}{3.1536}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0992493151\approx9.9249 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(year\right)\approx{\color{rgb(20,165,174)} 9.9249 \times 10^{-2}}\left(decade\right)\)
