Convert lambda to board foot
Learn how to convert
1
lambda to
board foot
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(lambda\right)={\color{rgb(20,165,174)} x}\left(board \text{ } foot\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(lambda\right) = {\color{rgb(89,182,91)} 10^{-9}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 10^{-9}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(board \text{ } foot\right) = {\color{rgb(125,164,120)} 2.359737216 \times 10^{-3}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 2.359737216 \times 10^{-3}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(lambda\right)={\color{rgb(20,165,174)} x}\left(board \text{ } foot\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.359737216 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.359737216 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.359737216 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-9} = {\color{rgb(20,165,174)} x} \times 2.359737216 \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancelto{10^{-6}}{10^{-9}}} = {\color{rgb(20,165,174)} x} \times 2.359737216 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(\text{Simplify}\)
\(10^{-6} = {\color{rgb(20,165,174)} x} \times 2.359737216\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.359737216 = 10^{-6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.359737216}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.359737216 \times \dfrac{1.0}{2.359737216} = 10^{-6} \times \dfrac{1.0}{2.359737216}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.359737216}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.359737216}}} = 10^{-6} \times \dfrac{1.0}{2.359737216}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-6}}{2.359737216}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000004238\approx4.2378 \times 10^{-7}\)
\(\text{Conversion Equation}\)
\(1.0\left(lambda\right)\approx{\color{rgb(20,165,174)} 4.2378 \times 10^{-7}}\left(board \text{ } foot\right)\)
