Convert gram / square inch to ounce / square yard
Learn how to convert
1
gram / square inch to
ounce / square yard
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{gram}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{ounce}{square \text{ } yard}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(pascal\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{gram}{square \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}\left(pascal\right)} = {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}\left(Pa\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{ounce}{square \text{ } yard}\right) = {\color{rgb(125,164,120)} \dfrac{2.78013850953781}{8.3612736}\left(pascal\right)} = {\color{rgb(125,164,120)} \dfrac{2.78013850953781}{8.3612736}\left(Pa\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{gram}{square \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{ounce}{square \text{ } yard}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \times {\color{rgb(89,182,91)} \left(pascal\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.78013850953781}{8.3612736}}} \times {\color{rgb(125,164,120)} \left(pascal\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \cdot {\color{rgb(89,182,91)} \left(Pa\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.78013850953781}{8.3612736}} \cdot {\color{rgb(125,164,120)} \left(Pa\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{9.80665}{6.4516 \times 10^{-1}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Pa\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.78013850953781}{8.3612736}} \times {\color{rgb(125,164,120)} \cancel{\left(Pa\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{9.80665}{6.4516 \times 10^{-1}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.78013850953781}{8.3612736}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.78013850953781}{8.3612736} = \dfrac{9.80665}{6.4516 \times 10^{-1}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{8.3612736}{2.78013850953781}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.78013850953781}{8.3612736} \times \dfrac{8.3612736}{2.78013850953781} = \dfrac{9.80665}{6.4516 \times 10^{-1}} \times \dfrac{8.3612736}{2.78013850953781}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.78013850953781}} \times {\color{rgb(99,194,222)} \cancel{8.3612736}}}{{\color{rgb(99,194,222)} \cancel{8.3612736}} \times {\color{rgb(255,204,153)} \cancel{2.78013850953781}}} = \dfrac{9.80665 \times 8.3612736}{6.4516 \times 10^{-1} \times 2.78013850953781}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{9.80665 \times 8.3612736}{6.4516 \times 10^{-1} \times 2.78013850953781}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0 \times 9.80665 \times 8.3612736}{6.4516 \times 2.78013850953781}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx45.715054687\approx45.7151\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{gram}{square \text{ } inch}\right)\approx{\color{rgb(20,165,174)} 45.7151}\left(\dfrac{ounce}{square \text{ } yard}\right)\)
