Convert gram-force • inch to dyne • meter
Learn how to convert
1
gram-force • inch to
dyne • meter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gram-force \times inch\right)={\color{rgb(20,165,174)} x}\left(dyne \times meter\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton \times meter\right)\)
\(\text{Left side: 1.0 } \left(gram-force \times inch\right) = {\color{rgb(89,182,91)} 2.4908891 \times 10^{-4}\left(newton \times meter\right)} = {\color{rgb(89,182,91)} 2.4908891 \times 10^{-4}\left(N \cdot m\right)}\)
\(\text{Right side: 1.0 } \left(dyne \times meter\right) = {\color{rgb(125,164,120)} 10^{-5}\left(newton \times meter\right)} = {\color{rgb(125,164,120)} 10^{-5}\left(N \cdot m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gram-force \times inch\right)={\color{rgb(20,165,174)} x}\left(dyne \times meter\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.4908891 \times 10^{-4}} \times {\color{rgb(89,182,91)} \left(newton \times meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-5}}} \times {\color{rgb(125,164,120)} \left(newton \times meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.4908891 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(N \cdot m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-5}} \cdot {\color{rgb(125,164,120)} \left(N \cdot m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.4908891 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N \cdot m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-5}} \times {\color{rgb(125,164,120)} \cancel{\left(N \cdot m\right)}}\)
\(\text{Conversion Equation}\)
\(2.4908891 \times 10^{-4} = {\color{rgb(20,165,174)} x} \times 10^{-5}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(2.4908891 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-5}}}\)
\(\text{Simplify}\)
\(2.4908891 = {\color{rgb(20,165,174)} x} \times 10^{-1}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-1} = 2.4908891\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-1} \times \dfrac{1.0}{10^{-1}} = 2.4908891 \times \dfrac{1.0}{10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-1}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-1}}}} = 2.4908891 \times \dfrac{1.0}{10^{-1}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.4908891}{10^{-1}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10.0 \times 2.4908891\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 24.908891\approx24.9089\)
\(\text{Conversion Equation}\)
\(1.0\left(gram-force \times inch\right)\approx{\color{rgb(20,165,174)} 24.9089}\left(dyne \times meter\right)\)
