Use scientific notation to determine which of these numbers has the greatest value: 654,987,034: 645,897,430; or 546,789,340. Write your answer in scientific notation, expressed to the exact decimal place.

1 answer

To express the given numbers in scientific notation, we convert each number into a form that is a coefficient multiplied by 10 raised to an exponent.

  1. For 654,987,034:

    • Move the decimal point 8 places to the left: \[ 654,987,034 = 6.54987034 \times 10^8 \]
  2. For 645,897,430:

    • Move the decimal point 8 places to the left: \[ 645,897,430 = 6.45897430 \times 10^8 \]
  3. For 546,789,340:

    • Move the decimal point 8 places to the left: \[ 546,789,340 = 5.46789340 \times 10^8 \]

Now, we can compare the coefficients, since they all have the same exponent of \(10^8\):

  • \(6.54987034\) (for 654,987,034)
  • \(6.45897430\) (for 645,897,430)
  • \(5.46789340\) (for 546,789,340)

The largest coefficient is \(6.54987034\), which corresponds to \(654,987,034\).

Thus, the number with the greatest value is \(654,987,034\), and in scientific notation, it is: \[ \boxed{6.54987034 \times 10^8} \]