Convert gram-force • meter to dyne • meter

Learn how to convert 1 gram-force • meter to dyne • meter step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(gram-force \times meter\right)={\color{rgb(20,165,174)} x}\left(dyne \times meter\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton \times meter\right)\)
\(\text{Left side: 1.0 } \left(gram-force \times meter\right) = {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}\left(newton \times meter\right)} = {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}\left(N \cdot m\right)}\)
\(\text{Right side: 1.0 } \left(dyne \times meter\right) = {\color{rgb(125,164,120)} 10^{-5}\left(newton \times meter\right)} = {\color{rgb(125,164,120)} 10^{-5}\left(N \cdot m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gram-force \times meter\right)={\color{rgb(20,165,174)} x}\left(dyne \times meter\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left(newton \times meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-5}}} \times {\color{rgb(125,164,120)} \left(newton \times meter\right)}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(N \cdot m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-5}} \cdot {\color{rgb(125,164,120)} \left(N \cdot m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 9.80665 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N \cdot m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-5}} \times {\color{rgb(125,164,120)} \cancel{\left(N \cdot m\right)}}\)
\(\text{Conversion Equation}\)
\(9.80665 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 10^{-5}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(9.80665 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}}\)
\(9.80665 = {\color{rgb(20,165,174)} x} \times 10^{-2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-2} = 9.80665\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-2} \times \dfrac{1.0}{10^{-2}} = 9.80665 \times \dfrac{1.0}{10^{-2}}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-2}}}} = 9.80665 \times \dfrac{1.0}{10^{-2}}\)
\({\color{rgb(20,165,174)} x} = \dfrac{9.80665}{10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\({\color{rgb(20,165,174)} x} = 10^{2} \times 9.80665\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 980.665\approx9.8066 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(gram-force \times meter\right)\approx{\color{rgb(20,165,174)} 9.8066 \times 10^{2}}\left(dyne \times meter\right)\)

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