Weight Units: Using variables

In one kilometer there are 1000 meters,

therefore one meter is one-thousandth of a kilometer.

To convert $x^2$ kilograms to grams, follow these steps:

• Step 1: Start from the given expression in kilograms, which is $x^2 \text{ kg}$.
• Step 2: Use the conversion factor: $1 \text{ kg} = 1000 \text{ gr}$.
• Step 3: Multiply the given $x^2$ by 1000 to convert it into grams.

Performing the multiplication, we have:
$x^2 \times 1000 = 1000x^2$

Therefore, the weight in grams is $1000x^2$.

The correct choice corresponding to this result is:

• Choice 1: $1000x^2$

In summary, the equivalent of $x^2$ kilograms in grams is $1000x^2$.

To convert the given expression from kilograms to tons, we need to follow these steps:

• Step 1: Express the weight in kilograms. The given expression is $x^2 \times 100 \text{ kg}$.
• Step 2: Convert kilograms to tons by dividing by 1000, because $1 \text{ ton} = 1000 \text{ kg}$.

Now, implementing these steps, we first have the expression in kilograms:
$x^2 \times 100 \text{ kg}$

To convert this to tons, divide by 1000:
$\frac{x^2 \times 100}{1000}$

Simplify the expression:
$= \frac{x^2}{10}$

This result shows that the expression $x^2 \times 100 \text{ kg}$ is equivalent to $\frac{x^2}{10} \text{ tons}$.

Therefore, the correct answer is:

$\frac{x^2}{10}$