Convert quarter to pennyweight

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

Calculation Breakdown

Set up the equation

1.0 (q u a r t e r) = x (p e n n y w e i g h t)

Define the base values of the selected units in relation to the SI unit

(k i l o g r a m)

Left side: 1.0 (q u a r t e r) = 12.70058636 (k i l o g r a m) = 12.70058636 (k g)

Right side: 1.0 (p e n n y w e i g h t) = 1.55517384 \times 10^{- 3} (k i l o g r a m) = 1.55517384 \times 10^{- 3} (k g)

Insert known values into the conversion equation to determine

x

1.0 (q u a r t e r) = x (p e n n y w e i g h t)

Insert known values =>

1.0 \times 12.70058636 \times (k i l o g r a m) = x \times 1.55517384 \times 10^{- 3} \times (k i l o g r a m)

Or

1.0 \cdot 12.70058636 \cdot (k g) = x \cdot 1.55517384 \times 10^{- 3} \cdot (k g)

Cancel SI units

1.0 \times 12.70058636 \cdot (k g) = x \times 1.55517384 \times 10^{- 3} \times (k g)

Conversion Equation

12.70058636 = x \times 1.55517384 \times 10^{- 3}

Switch sides

x \times 1.55517384 \times 10^{- 3} = 12.70058636

Isolate

x

Multiply both sides by

(\frac{1.0}{1.55517384 \times 10^{- 3}})

x \times 1.55517384 \times 10^{- 3} \times \frac{1.0}{1.55517384 \times 10^{- 3}} = 12.70058636 \times \frac{1.0}{1.55517384 \times 10^{- 3}}

Cancel

x \times 1.55517384 \times 10^{- 3} \times \frac{1.0}{1.55517384 \times 10^{- 3}} = 12.70058636 \times \frac{1.0}{1.55517384 \times 10^{- 3}}

Simplify

x = \frac{12.70058636}{1.55517384 \times 10^{- 3}}

Rewrite equation

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

Rewrite

x = \frac{10^{3} \times 12.70058636}{1.55517384}

Solve

x

x \approx 8166.6666667 \approx 8.1667 \times 10^{3}

Conversion Equation

1.0 (q u a r t e r) \approx 8.1667 \times 10^{3} (p e n n y w e i g h t)

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