Convert gram-force • foot to gram-force • inch
Learn how to convert
1
gram-force • foot to
gram-force • inch
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gram-force \times foot\right)={\color{rgb(20,165,174)} x}\left(gram-force \times inch\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton \times meter\right)\)
\(\text{Left side: 1.0 } \left(gram-force \times foot\right) = {\color{rgb(89,182,91)} 2.98906692 \times 10^{-3}\left(newton \times meter\right)} = {\color{rgb(89,182,91)} 2.98906692 \times 10^{-3}\left(N \cdot m\right)}\)
\(\text{Right side: 1.0 } \left(gram-force \times inch\right) = {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}\left(newton \times meter\right)} = {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}\left(N \cdot m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gram-force \times foot\right)={\color{rgb(20,165,174)} x}\left(gram-force \times inch\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.98906692 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left(newton \times meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left(newton \times meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.98906692 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(N \cdot m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left(N \cdot m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.98906692 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N \cdot m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.4908891 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left(N \cdot m\right)}}\)
\(\text{Conversion Equation}\)
\(2.98906692 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(2.98906692 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times 2.4908891 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-4}}}\)
\(\text{Simplify}\)
\(2.98906692 = {\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-1}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-1} = 2.98906692\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.4908891 \times 10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.4908891 \times 10^{-1} \times \dfrac{1.0}{2.4908891 \times 10^{-1}} = 2.98906692 \times \dfrac{1.0}{2.4908891 \times 10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.4908891}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.4908891}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}} = 2.98906692 \times \dfrac{1.0}{2.4908891 \times 10^{-1}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.98906692}{2.4908891 \times 10^{-1}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0 \times 2.98906692}{2.4908891}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 12\)
\(\text{Conversion Equation}\)
\(1.0\left(gram-force \times foot\right) = {\color{rgb(20,165,174)} 12}\left(gram-force \times inch\right)\)
