Convert carat to grain

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

Calculation Breakdown

Set up the equation

1.0 (c a r a t) = x (g r a i n)

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 (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)

Right side: 1.0 (g r a i n) = 6.479891 \times 10^{- 5} (k i l o g r a m) = 6.479891 \times 10^{- 5} (k g)

Insert known values into the conversion equation to determine

x

1.0 (c a r a t) = x (g r a i n)

Insert known values =>

1.0 \times 2.0 \times 10^{- 4} \times (k i l o g r a m) = x \times 6.479891 \times 10^{- 5} \times (k i l o g r a m)

Or

1.0 \cdot 2.0 \times 10^{- 4} \cdot (k g) = x \cdot 6.479891 \times 10^{- 5} \cdot (k g)

Cancel SI units

1.0 \times 2.0 \times 10^{- 4} \cdot (k g) = x \times 6.479891 \times 10^{- 5} \times (k g)

Conversion Equation

2.0 \times 10^{- 4} = x \times 6.479891 \times 10^{- 5}

Cancel factors on both sides

Cancel factors

2.0 \times 10^{- 4} = x \times 6.479891 \times {10^{- 5}}^{10^{- 1}}

Simplify

2.0 = x \times 6.479891 \times 10^{- 1}

Switch sides

x \times 6.479891 \times 10^{- 1} = 2.0

Isolate

x

Multiply both sides by

(\frac{1.0}{6.479891 \times 10^{- 1}})

x \times 6.479891 \times 10^{- 1} \times \frac{1.0}{6.479891 \times 10^{- 1}} = 2.0 \times \frac{1.0}{6.479891 \times 10^{- 1}}

Cancel

x \times 6.479891 \times 10^{- 1} \times \frac{1.0}{6.479891 \times 10^{- 1}} = 2.0 \times \frac{1.0}{6.479891 \times 10^{- 1}}

Simplify

x = \frac{2.0}{6.479891 \times 10^{- 1}}

Rewrite equation

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

Rewrite

x = \frac{10.0 \times 2.0}{6.479891}

Solve

x

x \approx 3.0864716706 \approx 3.0865

Conversion Equation

1.0 (c a r a t) \approx 3.0865 (g r a i n)

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