To express Avogadro's number, [tex]\(602,200,000,000,000,000,000,000\)[/tex], in scientific notation, we follow these steps:
1. Identify the Significant Figures:
We want to express the number using only significant figures. The significant digits in this number are 6, 0, 2, and 2.
2. Place the Decimal Point:
Adjust the number so that it falls in the range of 1 to 10 by placing the decimal point after the first significant figure. Therefore, [tex]$602,200,000,000,000,000,000,000$[/tex] becomes [tex]$6.022$[/tex].
3. Count the Decimal Places:
Count the number of decimal places from the new position of the decimal point back to its original position at the end of the number. Here, the decimal point has moved 23 places to the left.
4. Compose the Term in Scientific Notation:
Multiply the significant figure by 10 raised to the power of the number of places moved. This gives us [tex]$6.022 \times 10^{23}$[/tex].
5. Rounding (if applicable):
Often Avogadro's number is rounded to three significant digits, which is commonly seen as [tex]$6.02$[/tex].
So, the number in scientific notation is [tex]$6.02 \times 10^{23}$[/tex].
Reviewing the given choices:
A. [tex]\(\frac{6.02}{10^{23}}\)[/tex] - This represents a much smaller number, not Avogadro's number.
B. [tex]\(\frac{1}{6.02 \times 10^{23}}\)[/tex] - This represents the reciprocal of Avogadro's number.
C. [tex]\(6.02 / 10^{23}\)[/tex] - This is another way of writing a much smaller number.
D. [tex]\(6.02 \times 10^{23}\)[/tex] - This matches our scientific notation for Avogadro's number.
E. [tex]\(6.02 \times 10^{-23}\)[/tex] - This represents an extremely small number.
The correct answer is thus D. [tex]\(6.02 \times 10^{23}\)[/tex].
