Convert dog watch to year
Learn how to convert
1
dog watch to
year
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(dog \text{ } watch\right)={\color{rgb(20,165,174)} x}\left(year\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(second\right)\)
\(\text{Left side: 1.0 } \left(dog \text{ } watch\right) = {\color{rgb(89,182,91)} 7.2 \times 10^{3}\left(second\right)} = {\color{rgb(89,182,91)} 7.2 \times 10^{3}\left(s\right)}\)
\(\text{Right side: 1.0 } \left(year\right) = {\color{rgb(125,164,120)} 3.16224 \times 10^{7}\left(second\right)} = {\color{rgb(125,164,120)} 3.16224 \times 10^{7}\left(s\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(dog \text{ } watch\right)={\color{rgb(20,165,174)} x}\left(year\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 7.2 \times 10^{3}} \times {\color{rgb(89,182,91)} \left(second\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.16224 \times 10^{7}}} \times {\color{rgb(125,164,120)} \left(second\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 7.2 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \left(s\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.16224 \times 10^{7}} \cdot {\color{rgb(125,164,120)} \left(s\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 7.2 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(s\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.16224 \times 10^{7}} \times {\color{rgb(125,164,120)} \cancel{\left(s\right)}}\)
\(\text{Conversion Equation}\)
\(7.2 \times 10^{3} = {\color{rgb(20,165,174)} x} \times 3.16224 \times 10^{7}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(7.2 \times {\color{rgb(255,204,153)} \cancel{10^{3}}} = {\color{rgb(20,165,174)} x} \times 3.16224 \times {\color{rgb(255,204,153)} \cancelto{10^{4}}{10^{7}}}\)
\(\text{Simplify}\)
\(7.2 = {\color{rgb(20,165,174)} x} \times 3.16224 \times 10^{4}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.16224 \times 10^{4} = 7.2\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.16224 \times 10^{4}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.16224 \times 10^{4} \times \dfrac{1.0}{3.16224 \times 10^{4}} = 7.2 \times \dfrac{1.0}{3.16224 \times 10^{4}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.16224}} \times {\color{rgb(99,194,222)} \cancel{10^{4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.16224}} \times {\color{rgb(99,194,222)} \cancel{10^{4}}}} = 7.2 \times \dfrac{1.0}{3.16224 \times 10^{4}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{7.2}{3.16224 \times 10^{4}}\)
Rewrite equation
\(\dfrac{1.0}{10^{4}}\text{ can be rewritten to }10^{-4}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-4} \times 7.2}{3.16224}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0002276867\approx2.2769 \times 10^{-4}\)
\(\text{Conversion Equation}\)
\(1.0\left(dog \text{ } watch\right)\approx{\color{rgb(20,165,174)} 2.2769 \times 10^{-4}}\left(year\right)\)
