Question

Use scientific notation to determine which of these numbers has the least value: 98,789,000; 987,890,000; or 89,987,000. Write your answer in scientific notation, expressed to the exact decimal place.

1 answer

To express the numbers in scientific notation, we need to convert each number into the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer representing the power of ten.

  1. For 98,789,000: \[ 98,789,000 = 9.8789 \times 10^7 \]

  2. For 987,890,000: \[ 987,890,000 = 9.8789 \times 10^8 \]

  3. For 89,987,000: \[ 89,987,000 = 8.9987 \times 10^7 \]

Now we can compare the values. The exponents tell us that:

  • \( 9.8789 \times 10^7 \) is in the 10 million range,
  • \( 9.8789 \times 10^8 \) is in the 100 million range,
  • \( 8.9987 \times 10^7 \) is also in the 10 million range.

To directly compare \( 9.8789 \times 10^7 \) and \( 8.9987 \times 10^7 \):

  • \( 9.8789 \times 10^7 \) (98,789,000)
  • \( 8.9987 \times 10^7 \) (89,987,000)

Since \( 8.9987 < 9.8789 \), we can conclude that:

  • \( 89,987,000 \) has the least value among the three numbers.

In summary, the number with the least value expressed in scientific notation is: \[ \boxed{8.9987 \times 10^7} \]