Question

Scientific Notation Unit Test
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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.

Answer 1

To compare the given numbers in scientific notation, we will convert each of them to that format.

1. **98,789,000**:
- To convert to scientific notation:
\( 98,789,000 = 9.8789 \times 10^7 \)

2. **987,890,000**:
- To convert to scientific notation:
\( 987,890,000 = 9.8789 \times 10^8 \)

3. **89,987,000**:
- To convert to scientific notation:
\( 89,987,000 = 8.9987 \times 10^7 \)

Now, let's compare these scientific notations:

- \( 9.8789 \times 10^7 \)
- \( 9.8789 \times 10^8 \)
- \( 8.9987 \times 10^7 \)

To determine which has the least value, we can compare the powers of ten first. The number with the smallest exponent will be smaller if the coefficients are comparable.

1. **Compare the powers of ten**:
- \( 9.8789 \times 10^8 \) has the highest power, so it's the largest.
- Comparing \( 9.8789 \times 10^7 \) and \( 8.9987 \times 10^7 \), both have the same power of \( 10^7 \).

2. **Compare the coefficients**:
- \( 9.8789 \) vs. \( 8.9987 \):
\( 8.9987 \) is less than \( 9.8789 \).

Thus, the number with the least value among the three is **89,987,000** expressed as **\( 8.9987 \times 10^7 \)** in scientific notation.