To express Avogadro's number, which is approximately 602,200,000,000,000,000,000,000, in scientific notation, we need to rewrite it as a product of a number between 1 and 10 and a power of 10.
Here are the detailed steps:
1. Identify the Significant Figures: The number we are working with is 602,200,000,000,000,000,000,000. The significant figures in this number are '6.022'.
2. Position the Decimal Point:
- Place the decimal point right after the first digit, which gives us 6.022.
3. Count the Decimal Places:
- Count how many places the decimal point needs to move to convert the original number into a number between 1 and 10. In this case, the decimal must move 23 places to the left.
4. Construct the Scientific Notation:
- When the decimal is moved 23 places to the left, it's equivalent to multiplying by [tex]\(10^{23}\)[/tex].
Putting this together:
- The number 602,200,000,000,000,000,000,000 is written in scientific notation as [tex]\(6.022 \times 10^{23}\)[/tex].
Now we can match this with the given options:
A. [tex]\(\frac{6.02}{10^{23}}\)[/tex]
B. [tex]\(\frac{1}{6.02 \times 10^{23}}\)[/tex]
C. [tex]\(6.02 / 10^{23}\)[/tex]
D. [tex]\(6.02 \times 10^{23}\)[/tex]
E. [tex]\(6.02 \times 10^{-23}\)[/tex]
The correct scientific notation for Avogadro's number is:
[tex]\[ \boxed{6.02 \times 10^{23}} \][/tex]
Therefore, the correct option is D [tex]\(6.02 \times 10^{23}\)[/tex].
