To compare the numbers 654,987,034, 645,897,430, and 546,789,340 using scientific notation, we first express each number in scientific notation:
- \( 654,987,034 = 6.54987034 \times 10^8 \)
- \( 645,897,430 = 6.45897430 \times 10^8 \)
- \( 546,789,340 = 5.46789340 \times 10^8 \)
Now we can compare the coefficients (the numbers before the \( \times 10^8 \)) to determine which is greatest.
- \( 6.54987034 \)
- \( 6.45897430 \)
- \( 5.46789340 \)
Clearly, \( 6.54987034 \) is the greatest.
Thus, the number with the greatest value among the three given numbers in scientific notation is:
\[ \boxed{6.54987034 \times 10^8} \]