Convert Carat to Kilogram
Unit definitions
Carat
$\frac{2}{10}$ of a gram is a carat. It is used to measure the mass of gemstones.
Kilogram
The kilogram is the SI base unit of mass. Since the 2019 redefinition of the SI base units, it is defined by using the fixed numerical value of the Planck's constant ($h$) to be $6.626\,070\,15 \times 10^{-34} \ \text{J}\text{s}$. $$h = 6.626\,070\,15 \times 10^{-34} \ \text{J}\text{s}$$ $$h = 6.626\,070\,15 \times 10^{-34} \ \text{kg}\text{m}^2\text{s}^{-2}\cdot\text{s}$$ $$h = 6.626\,070\,15 \times 10^{-34} \ \text{kg}\text{m}^2\text{s}^{-1}$$ Therefore, $$1 \ \text{kg} = \frac{h}{6.626\,070\,15 \times 10^{-34} \ \text{m}^2\text{s}^{-1}}$$ $$1 \ \text{kg} = \frac{h}{6.626\,070\,15 \times 10^{-34}} \ \text{m}^{-2} \text{s}$$
How to convert Carat to Kilogram
$$\text{Mass}_{\text{kg}} = \frac{\text{Mass}_{\text{ct}}}{5000}$$
Examples
Example 1
Convert $30.0\ \text{ct}$ to $\text{kg}$.
$$\text{Mass}_{\text{kg}} = \frac{30.0}{5000}$$
$$\text{Mass}_{\text{kg}} = 0.006$$
$$\therefore \ 30.0\ \text{ct} = 0.006 \ \text{kg}$$
Example 2
Convert $80.0\ \text{ct}$ to $\text{kg}$.
$$\text{Mass}_{\text{kg}} = \frac{80.0}{5000}$$
$$\text{Mass}_{\text{kg}} = 0.016$$
$$\therefore \ 80.0\ \text{ct} = 0.016 \ \text{kg}$$
Example 3
Convert $120.0\ \text{ct}$ to $\text{kg}$.
$$\text{Mass}_{\text{kg}} = \frac{120.0}{5000}$$
$$\text{Mass}_{\text{kg}} = 0.024$$
$$\therefore \ 120.0\ \text{ct} = 0.024 \ \text{kg}$$
Example 4
Convert $145.0\ \text{ct}$ to $\text{kg}$.
$$\text{Mass}_{\text{kg}} = \frac{145.0}{5000}$$
$$\text{Mass}_{\text{kg}} = 0.029$$
$$\therefore \ 145.0\ \text{ct} = 0.029 \ \text{kg}$$
Example 5
Convert $185.0\ \text{ct}$ to $\text{kg}$.
$$\text{Mass}_{\text{kg}} = \frac{185.0}{5000}$$
$$\text{Mass}_{\text{kg}} = 0.037$$
$$\therefore \ 185.0\ \text{ct} = 0.037 \ \text{kg}$$