To express Jupiter's mass in scientific notation, let's carefully break down each step:
1. Understand Scientific Notation: Scientific notation represents a number as a product of two parts:
- A decimal part, typically between 1 and 10 (but not including 10).
- An exponent of 10, indicating the power to which 10 is raised.
2. Given Mass: The mass of Jupiter is [tex]\(1,898,000,000,000,000,000,000,000,000 \text{ kg}\)[/tex].
3. Identify Leading Digits: The significant figures are 1.898.
4. Count the Digits: Count how many places the decimal point needs to be moved to position just after the first digit:
- Start from the end of the number and move 27 places to the left to place the decimal point after 1.898. This means the exponent will be 27.
Thus, Jupiter's mass expressed in scientific notation is:
[tex]\[ 1.898 \times 10^{27} \text{ kg} \][/tex]
5. Evaluate the Choices:
- A: [tex]\(1.898 \times 10^{24} \text{ kg}\)[/tex] (incorrect, exponent is wrong)
- B: [tex]\(189.8 \times 10^{27} \text{ kg}\)[/tex] (incorrect, not in proper scientific notation format—should be between 1 and 10)
- C: [tex]\(1.898^{27} \text{ kg}\)[/tex] (incorrect, incorrectly formatted, not scientific notation)
- D: [tex]\(1.898 \times 10^{27} \text{ kg}\)[/tex] (correct, matches our calculation)
Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
