Convert tonne to carat

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

Calculation Breakdown

Set up the equation

1.0 (t o n n e) = 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 (t o n n e) = 1016.0469088 (k i l o g r a m) = 1016.0469088 (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 (t o n n e) = x (c a r a t)

Insert known values =>

1.0 \times 1016.0469088 \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 1016.0469088 \cdot (k g) = x \cdot 2.0 \times 10^{- 4} \cdot (k g)

Cancel SI units

1.0 \times 1016.0469088 \cdot (k g) = x \times 2.0 \times 10^{- 4} \times (k g)

Conversion Equation

1016.0469088 = x \times 2.0 \times 10^{- 4}

Switch sides

x \times 2.0 \times 10^{- 4} = 1016.0469088

Isolate

x

Multiply both sides by

(\frac{1.0}{2.0 \times 10^{- 4}})

x \times 2.0 \times 10^{- 4} \times \frac{1.0}{2.0 \times 10^{- 4}} = 1016.0469088 \times \frac{1.0}{2.0 \times 10^{- 4}}

Cancel

x \times 2.0 \times 10^{- 4} \times \frac{1.0}{2.0 \times 10^{- 4}} = 1016.0469088 \times \frac{1.0}{2.0 \times 10^{- 4}}

Simplify

x = \frac{1016.0469088}{2.0 \times 10^{- 4}}

Rewrite equation

\frac{1.0}{10^{- 4}} can be rewritten to 10^{4}

Rewrite

x = \frac{10^{4} \times 1016.0469088}{2.0}

Solve

x

x = 5080234.544 \approx 5.0802 \times 10^{6}

Conversion Equation

1.0 (t o n n e) \approx 5.0802 \times 10^{6} (c a r a t)

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