use scientific notation to determine which of these numbers has the least value: 86,659,000; 867,450,000; or 86,423,00. write your answer in scientific notation expressed to the exact decimal place.

1 answer

To express each of the numbers in scientific notation, we need to write them in the form of \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.

  1. For 86,659,000:

    • Move the decimal point 7 places to the left.
    • \( 86,659,000 = 8.6659 \times 10^7 \)
  2. For 867,450,000:

    • Move the decimal point 8 places to the left.
    • \( 867,450,000 = 8.6745 \times 10^8 \)
  3. For 86,423,000:

    • Move the decimal point 7 places to the left.
    • \( 86,423,000 = 8.6423 \times 10^7 \)

Now, let's compare the numbers in scientific notation:

  • \( 8.6659 \times 10^7 \) (for 86,659,000)
  • \( 8.6745 \times 10^8 \) (for 867,450,000)
  • \( 8.6423 \times 10^7 \) (for 86,423,000)

The powers of 10 indicate the scale of the numbers:

  • \( 8.6659 \times 10^7 \) and \( 8.6423 \times 10^7 \) are both multiplied by \( 10^7 \), while \( 8.6745 \times 10^8 \) is multiplied by \( 10^8 \), making it much larger.

Among \( 8.6659 \times 10^7 \) and \( 8.6423 \times 10^7 \):

  • \( 8.6423 < 8.6659 \)

Thus, among the three numbers, the number with the least value is 86,423,000, which in scientific notation is:

\[ \boxed{8.6423 \times 10^7} \]