To express the mass of Jupiter, [tex]\(1,898,000,000,000,000,000,000,000,000 kg\)[/tex], in scientific notation, follow these steps:
1. Identify the significant figures:
The number [tex]\(1,898,000,000,000,000,000,000,000,000\)[/tex] is large but can be broken down to highlight its significant figures. Here, it consists of the digits [tex]\(1.898\)[/tex] followed by numerous zeros.
2. Determine the appropriate power of 10:
To properly represent the number in scientific notation, we need to place the decimal after the first significant digit and multiply by the appropriate power of 10.
- Move the decimal point in [tex]\(1,898,000,000,000,000,000,000,000,000\)[/tex] to the left until it is between the 1 and the 8 (this becomes [tex]\(1.898\)[/tex]).
- Count the number of decimal places moved. Starting from the rightmost digit, we move the decimal point 27 places to the left to position the decimal after the 1.
3. Combine the two parts:
Putting it all together, the number [tex]\(1,898,000,000,000,000,000,000,000,000\)[/tex] becomes:
[tex]\[
1.898 \times 10^{27}
\][/tex]
Thus, the correct representation of Jupiter's mass in scientific notation is:
[tex]\[
1.898 \times 10^{27} \, \text{kg}
\][/tex]
Finally, by comparing with the given options:
A. [tex]\(189.8 \times 10^{27} \, \text{kg}\)[/tex]
B. [tex]\(1.898 \times 10^{24} \, \text{kg}\)[/tex]
C. [tex]\(1.898 \times 10^{27} \, \text{kg}\)[/tex]
D. [tex]\(1.898^{27} \, \text{kg}\)[/tex]
The correct answer is:
[tex]\[
\boxed{1.898 \times 10^{27} \, \text{kg}}
\][/tex]
So, the correct option is:
[tex]\[
\boxed{C}
\][/tex]
