Convert sack to pennyweight
Learn how to convert
1
sack to
pennyweight
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(sack\right)={\color{rgb(20,165,174)} x}\left(pennyweight\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(sack\right) = {\color{rgb(89,182,91)} 39.689332375\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 39.689332375\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(pennyweight\right) = {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(sack\right)={\color{rgb(20,165,174)} x}\left(pennyweight\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 39.689332375} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 39.689332375} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 39.689332375} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(39.689332375 = {\color{rgb(20,165,174)} x} \times 1.55517384 \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.55517384 \times 10^{-3} = 39.689332375\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.55517384 \times 10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.55517384 \times 10^{-3} \times \dfrac{1.0}{1.55517384 \times 10^{-3}} = 39.689332375 \times \dfrac{1.0}{1.55517384 \times 10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.55517384}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.55517384}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = 39.689332375 \times \dfrac{1.0}{1.55517384 \times 10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{39.689332375}{1.55517384 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 39.689332375}{1.55517384}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx25520.833333\approx2.5521 \times 10^{4}\)
\(\text{Conversion Equation}\)
\(1.0\left(sack\right)\approx{\color{rgb(20,165,174)} 2.5521 \times 10^{4}}\left(pennyweight\right)\)
