Convert pennyweight to carat

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

Calculation Breakdown

Set up the equation

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

Right side: 1.0 (c a r a t) = 2.5919564 \times 10^{- 4} (k i l o g r a m) = 2.5919564 \times 10^{- 4} (k g)

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times 1.55517384 \times 10^{- 3} \times (k i l o g r a m) = x \times 2.5919564 \times 10^{- 4} \times (k i l o g r a m)

Or

1.0 \cdot 1.55517384 \times 10^{- 3} \cdot (k g) = x \cdot 2.5919564 \times 10^{- 4} \cdot (k g)

Cancel SI units

1.0 \times 1.55517384 \times 10^{- 3} \cdot (k g) = x \times 2.5919564 \times 10^{- 4} \times (k g)

Conversion Equation

1.55517384 \times 10^{- 3} = x \times 2.5919564 \times 10^{- 4}

Cancel factors on both sides

Cancel factors

1.55517384 \times 10^{- 3} = x \times 2.5919564 \times {10^{- 4}}^{10^{- 1}}

Simplify

1.55517384 = x \times 2.5919564 \times 10^{- 1}

Switch sides

x \times 2.5919564 \times 10^{- 1} = 1.55517384

Isolate

x

Multiply both sides by

(\frac{1.0}{2.5919564 \times 10^{- 1}})

x \times 2.5919564 \times 10^{- 1} \times \frac{1.0}{2.5919564 \times 10^{- 1}} = 1.55517384 \times \frac{1.0}{2.5919564 \times 10^{- 1}}

Cancel

x \times 2.5919564 \times 10^{- 1} \times \frac{1.0}{2.5919564 \times 10^{- 1}} = 1.55517384 \times \frac{1.0}{2.5919564 \times 10^{- 1}}

Simplify

x = \frac{1.55517384}{2.5919564 \times 10^{- 1}}

Rewrite equation

\frac{1.0}{10^{- 1}} can be rewritten to 10

Rewrite

x = \frac{10.0 \times 1.55517384}{2.5919564}

Solve

x

x = 6

Conversion Equation

1.0 (p e n n y w e i g h t) = 6 (c a r a t)

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