To find how many grams are in 1 kilogram, we can use the basic principles of unit conversion. Here's a detailed, step-by-step explanation:
1. Understand the Units: A kilogram (kg) is a unit of mass in the metric system, and it is larger than a gram (g). To convert from kilograms to grams, we need to know the conversion factor.
2. Conversion Factor: The metric system is based on powers of 10. Specifically, 1 kilogram is equal to 1000 grams. This is a standardized conversion factor.
3. Apply the Conversion Factor: To convert 1 kilogram to grams, you multiply the number of kilograms by the conversion factor.
[tex]\[
1 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 1000 \, \text{g}
\][/tex]
So, 1 kilogram is equal to 1000 grams.
4. Choose the Correct Option: Given the options:
- 100 g or [tex]\(10^2\)[/tex] g
- 1000 g or [tex]\(10^3\)[/tex] g
- [tex]\(1 / 100\)[/tex] g or [tex]\(10^{-2}\)[/tex] g
- [tex]\(1 / 10\)[/tex] g or [tex]\(10^{-1}\)[/tex] g
The correct answer is "1000 g or [tex]\(10^3\)[/tex] g".
Therefore, there are 1000 grams in 1 kilogram. Thus the final answer is:
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
