To compare the numbers 654,987,034; 645,897,430; and 546,789,340 using scientific notation, we convert each number:
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654,987,034 can be expressed in scientific notation as: \[ 654,987,034 = 6.54987034 \times 10^8 \]
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645,897,430 can be expressed in scientific notation as: \[ 645,897,430 = 6.45897430 \times 10^8 \]
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546,789,340 can be expressed in scientific notation as: \[ 546,789,340 = 5.46789340 \times 10^8 \]
Now we can compare the numbers by examining the coefficients (the numbers before \( \times 10^8 \)):
- \( 6.54987034 \)
- \( 6.45897430 \)
- \( 5.46789340 \)
Among these coefficients, \( 6.54987034 \) is the largest.
Thus, the number with the greatest value is: \[ \boxed{6.54987034 \times 10^8} \]