When $5.5490 \times 10^{8}$ is correctly rounded to three significant figures the number becomes 5.55 $5.55 \times 10^{8}$ 555 554 $5.54 \times 10^{8}$

Step 1 ：The given number is \(5.5490 \times 10^{8}\).

Step 2 ：We are asked to round this number to three significant figures.

Step 3 ：In significant figures rounding, we look at the digit after the last significant figure (in this case, the fourth digit after the decimal point), and if it's 5 or more, we round up the last significant figure. If it's less than 5, we leave the last significant figure as it is.

Step 4 ：Applying this rule to our number, we find that the digit after the third significant figure is 9, which is more than 5. Therefore, we round up the third significant figure.

Step 5 ：Thus, when \(5.5490 \times 10^{8}\) is correctly rounded to three significant figures, the number becomes \(5.55 \times 10^{8}\).

Step 6 ：\(\boxed{5.55 \times 10^{8}}\) is the final answer.