Convert Fraction 7/21 × 100g to Kilograms: Step-by-Step Solution

To solve this problem, we follow these steps:

• Step 1: Simplify the fraction $\frac{7}{21}$.
• Step 2: Multiply the simplified fraction by 100 grams.
• Step 3: Convert the resulting grams to kilograms.

Let's work through each step:

Step 1: Simplify $\frac{7}{21}$:
Both 7 and 21 can be divided by their greatest common divisor, which is 7. Simplifying gives us:

$\frac{7}{21} = \frac{7 \div 7}{21 \div 7} = \frac{1}{3}$.

Step 2: Calculate $\frac{1}{3} \times 100$ grams:
Multiply to find the weight in grams:

$\frac{1}{3} \times 100 = \frac{100}{3} \approx 33.33$ grams.

Step 3: Convert grams to kilograms:
To convert grams to kilograms, divide by 1000:

$\frac{33.33}{1000} = 0.03333...$ kilograms.
This is expressed as a fraction equivalent to:

$\frac{1}{30}$ kilograms (after realizing rounding applies to a precise fractional representation).

Thus, the correct answer is $\frac{1}{30}$ kilograms.

Therefore, the solution to the problem is $\frac{1}{30}$ kg.