Weight Units - Examples, Exercises and Solutions

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information and conversion factor
• Step 2: Apply the conversion factor to obtain the result in grams

Let's work through these steps:
Step 1: We have $8.6 \, \text{kg}$ to convert to grams. Recall that $1 \, \text{kg}$ equals $1000 \, \text{grams}$.
Step 2: Multiply the given kilograms by the conversion factor to convert to grams:
$8.6 \, \text{kg} \times 1000 \, \text{grams/kg} = 8600 \, \text{grams}$

Therefore, the solution to the problem is $8600 \, \text{grams}$.

To solve this problem of converting kilograms to grams, we will follow these steps:

• Step 1: Identify the given weight in kilograms.
• Step 2: Use the conversion factor $1 \text{ kg} = 1000 \text{ g}$.
• Step 3: Perform the necessary multiplication.

Let's go through these steps in detail:
Step 1: We have been given a weight of $7$ kilograms.
Step 2: Recall that $1 \text{ kilogram} = 1000 \text{ grams}$.
Step 3: Multiply the number of kilograms by the conversion factor: $7 \text{ kg} \times 1000 \text{ g/kg} = 7000 \text{ g}$ This calculation confirms that $7$ kilograms is equivalent to $7000$ grams.

Therefore, the solution to the problem is $7000 \text{ grams}$.

The letter T indicates a metric tonne,

One tonne is equivalent to one thousand kilograms,

Therefore, in 7.8 tons there are

1000*7.8 = 7800 kg

To solve this problem, we will convert the weight from kilograms to grams.

We know that $1\, \text{kg} = 1,000\, \text{g}$. Therefore, to convert the weight from kilograms to grams, we multiply the weight in kilograms by 1,000.

With the given weight $3.21\, \text{kg}$, we perform the calculation as follows:

• Multiply $3.21$ by $1,000$:

$3.21 \times 1,000 = 3,210$

After performing this calculation, we find that $3.21 \, \text{kg}$ is equivalent to $3,210\, \text{g}$.

Therefore, the solution to the problem is $3,210$.

Comparing this result with the given multiple choice answers, the correct choice is option (3): $3,210$.

In one kilometer there are 1000 meters,

therefore one meter is one-thousandth of a kilometer.

First, let's simplify the fraction:

$\frac{55}{5}=11$

This leaves us with:

$11\times200kg$

Now, let's perform the calculation, giving us:

$2200kg$

Note that we need the answer in tons:

$T=1000kg$

$\frac{2200kg}{1000}=2.2T$

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.

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 solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number into a decimal.
• Step 2: Use the correct conversion factor to translate kilograms into metric tons.

Let's begin the conversion:

Step 1: Convert the given weight $387\frac{1}{4}$ kilograms into a decimal.
To convert $387\frac{1}{4}$, decode the mixed number: $\frac{1}{4} = 0.25$, so $387\frac{1}{4} = 387 + 0.25 = 387.25$ kg.

Step 2: Use the conversion factor $1 \text{ metric ton} = 1000 \text{ kg}$ to convert kilograms into metric tons.
Calculate by dividing the kilograms by 1000:
$387.25 \text{ kg} \div 1000 = 0.38725 \text{ metric tons}.$

Therefore, the weight of $387\frac{1}{4}$ kg is equivalent to $0.38725$ metric tons.

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:

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