Convert cubic yard to lambda
Learn how to convert
1
cubic yard to
lambda
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(cubic \text{ } yard\right)={\color{rgb(20,165,174)} x}\left(lambda\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(cubic \text{ } yard\right) = {\color{rgb(89,182,91)} 7.64554857984 \times 10^{-1}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 7.64554857984 \times 10^{-1}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(lambda\right) = {\color{rgb(125,164,120)} 10^{-9}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 10^{-9}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(cubic \text{ } yard\right)={\color{rgb(20,165,174)} x}\left(lambda\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 7.64554857984 \times 10^{-1}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-9}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 7.64554857984 \times 10^{-1}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-9}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 7.64554857984 \times 10^{-1}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-9}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(7.64554857984 \times 10^{-1} = {\color{rgb(20,165,174)} x} \times 10^{-9}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(7.64554857984 \times {\color{rgb(255,204,153)} \cancel{10^{-1}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{-8}}{10^{-9}}}\)
\(\text{Simplify}\)
\(7.64554857984 = {\color{rgb(20,165,174)} x} \times 10^{-8}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-8} = 7.64554857984\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-8}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-8} \times \dfrac{1.0}{10^{-8}} = 7.64554857984 \times \dfrac{1.0}{10^{-8}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-8}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-8}}}} = 7.64554857984 \times \dfrac{1.0}{10^{-8}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{7.64554857984}{10^{-8}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-8}}\text{ can be rewritten to }10^{8}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{8} \times 7.64554857984\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx764554857.98\approx7.6455 \times 10^{8}\)
\(\text{Conversion Equation}\)
\(1.0\left(cubic \text{ } yard\right)\approx{\color{rgb(20,165,174)} 7.6455 \times 10^{8}}\left(lambda\right)\)
