Convert liang(市兩) to carat

Learn how to convert 1 liang(市兩) to carat step by step.

Calculation Breakdown

Set up the equation

1.0 (l i a n g (市 兩)) = 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 (l i a n g (市 兩)) = 5.0 \times 10^{- 2} (k i l o g r a m) = 5.0 \times 10^{- 2} (k g)

Right side: 1.0 (c a r a t) = 2.0 \times 10^{- 4} (k i l o g r a m) = 2.0 \times 10^{- 4} (k g)

Insert known values into the conversion equation to determine

x

1.0 (l i a n g (市 兩)) = x (c a r a t)

Insert known values =>

1.0 \times 5.0 \times 10^{- 2} \times (k i l o g r a m) = x \times 2.0 \times 10^{- 4} \times (k i l o g r a m)

Or

1.0 \cdot 5.0 \times 10^{- 2} \cdot (k g) = x \cdot 2.0 \times 10^{- 4} \cdot (k g)

Cancel SI units

1.0 \times 5.0 \times 10^{- 2} \cdot (k g) = x \times 2.0 \times 10^{- 4} \times (k g)

Conversion Equation

5.0 \times 10^{- 2} = x \times 2.0 \times 10^{- 4}

Cancel factors on both sides

Cancel factors

5.0 \times 10^{- 2} = x \times 2.0 \times {10^{- 4}}^{10^{- 2}}

Simplify

5.0 = x \times 2.0 \times 10^{- 2}

Switch sides

x \times 2.0 \times 10^{- 2} = 5.0

Isolate

x

Multiply both sides by

(\frac{1.0}{2.0 \times 10^{- 2}})

x \times 2.0 \times 10^{- 2} \times \frac{1.0}{2.0 \times 10^{- 2}} = 5.0 \times \frac{1.0}{2.0 \times 10^{- 2}}

Cancel

x \times 2.0 \times 10^{- 2} \times \frac{1.0}{2.0 \times 10^{- 2}} = 5.0 \times \frac{1.0}{2.0 \times 10^{- 2}}

Simplify

x = \frac{5.0}{2.0 \times 10^{- 2}}

Rewrite equation

\frac{1.0}{10^{- 2}} can be rewritten to 10^{2}

Rewrite

x = \frac{10^{2} \times 5.0}{2.0}

Solve

x

x = 250 = 2.5 \times 10^{2}

Conversion Equation

1.0 (l i a n g (市 兩)) = 2.5 \times 10^{2} (c a r a t)

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