Question

Convert the following to the equivalent measures indicated. \(204 \mathrm{~g}=\) ______ \(\mathrm{kg}\)

Short answer

204 grams is 0.204 kilograms.

Step-by-step solution

Understand the Conversion Factor

To convert grams to kilograms, we need to know the conversion factor. There are 1000 grams in 1 kilogram. So, the conversion factor is 1 kg per 1000 g.

Set Up the Conversion Equation

We can set up an equation to convert 204 grams to kilograms using the conversion factor:\[ \text{kilograms} = 204 \text{ grams} \times \frac{1 \text{ kilogram}}{1000 \text{ grams}} \]

Perform the Calculation

Now, perform the calculation:\[ \text{kilograms} = 204 \times \frac{1}{1000} \]This simplifies to \( 204 \times 0.001 \), which equals 0.204 kilograms.

Write the Final Answer

Based on our calculation, 204 grams is equal to 0.204 kilograms.

Key concepts

Grams to Kilograms

Converting grams to kilograms is a common task in both science and everyday life. Grams and kilograms are both metric units of mass, but grams are often used for smaller weights, while kilograms are used for larger ones. Understanding this relationship is essential.
To make a conversion, we need to recognize that the metric system is based on powers of 10, which simplifies the process. Since 1 kilogram is composed of 1000 grams, we can easily convert between grams and kilograms by dividing the number of grams by 1000. This division moves the decimal point three places to the left, effectively converting grams to kilograms.

Conversion Factor

The conversion factor is a crucial element in converting units. It acts as a bridge between two different units that measures the same quantity. In this context, the conversion factor used to convert grams to kilograms is

• 1 kilogram per 1000 grams.

This conversion factor can be thought of as a multiplicative identity that helps us quickly and accurately convert grams to kilograms.
To use this factor, set up the conversion equation, where you multiply the number of grams by the conversion factor. It’s essential to ensure that the units you want to get rid of (grams, in this case) cancel out, leaving you with the desired units (kilograms).
Additionally, understanding the conversion factor helps you check your work since it provides a way to understand the relationship between both units clearly.

Mathematical Calculation

Performing the actual calculation to convert the units involves a straightforward mathematical process.
Once you have set up your conversion factor in the equation: \[ \text{kilograms} = \text{grams} \times \frac{1 \text{ kilogram}}{1000 \text{ grams}} \]you input the respective values.

• For 204 grams, the equation becomes: \[ 204 \times \frac{1}{1000} \]

This calculation simplifies to multiplying by 0.001.
The result of multiplying 204 by 0.001 equals 0.204 kilograms.
All steps ensure that numbers are handled accurately, maintaining precision in conversions, which is critical, especially in scientific calculations.