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.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 days ago

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:
\[
\boxed{8.9987 \times 10^7}
\]