# Convert pennyweight to ounce

Learn how to convert 1 pennyweight to ounce step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(pennyweight\right)={\color{rgb(20,165,174)} x}\left(ounce\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(pennyweight\right) = {\color{rgb(89,182,91)} 1.55517384 \times 10^{-3}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 1.55517384 \times 10^{-3}\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(ounce\right) = {\color{rgb(125,164,120)} 3.11034768 \times 10^{-2}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 3.11034768 \times 10^{-2}\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(pennyweight\right)={\color{rgb(20,165,174)} x}\left(ounce\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.55517384 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.11034768 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.55517384 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.11034768 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.55517384 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.11034768 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$1.55517384 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 3.11034768 \times 10^{-2}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$1.55517384 \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-3}}} = {\color{rgb(20,165,174)} x} \times 3.11034768 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}$$
$$\text{Simplify}$$
$$1.55517384 \times 10^{-1} = {\color{rgb(20,165,174)} x} \times 3.11034768$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 3.11034768 = 1.55517384 \times 10^{-1}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{3.11034768}\right)$$
$${\color{rgb(20,165,174)} x} \times 3.11034768 \times \dfrac{1.0}{3.11034768} = 1.55517384 \times 10^{-1} \times \dfrac{1.0}{3.11034768}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.11034768}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.11034768}}} = 1.55517384 \times 10^{-1} \times \dfrac{1.0}{3.11034768}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.55517384 \times 10^{-1}}{3.11034768}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 5 \times 10^{-2}$$
$$\text{Conversion Equation}$$
$$1.0\left(pennyweight\right) = {\color{rgb(20,165,174)} 5 \times 10^{-2}}\left(ounce\right)$$