To express a given large number in scientific notation, follow these steps:
1. Identify the significant figures: The given number is [tex]\( 1,898,000,000,000,000,000,000,000,000 \, \text{kg} \)[/tex]. The significant figures in this number are 1, 8, 9, and 8.
2. Place the decimal point after the first significant figure: Moving the decimal point after the first significant figure (1) converts the number to [tex]\( 1.898 \)[/tex].
3. Count the number of places the decimal point was moved to determine the exponent: The original number has 30 digits, so we move the decimal point 30 places to the left to place it after the first digit.
4. Express the number as a product of the significant figure and a power of 10: [tex]\( 1.898 \times 10^{30} \)[/tex].
Thus, the given mass of Jupiter in scientific notation is [tex]\( 1.898 \times 10^{30} \, \text{kg} \)[/tex].
Comparing this with the given options:
A. [tex]\( 1.898 \times 10^{24} \, \text{kg} \)[/tex]
B. [tex]\( 1.898^{27} \, \text{kg} \)[/tex]
C. [tex]\( 1.898 \times 10^{27} \, \text{kg} \)[/tex]
D. [tex]\( 189.8 \times 10^{27} \, \text{kg} \)[/tex]
The correct option that matches [tex]\( 1.898 \times 10^{30} \, \text{kg} \)[/tex] is C. Therefore, the answer is:
C. [tex]\( 1.898 \times 10^{30} \, \text{kg} \)[/tex]
