Scientific Notation Unit Test

Question

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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.(1 point)

Answer 1

To compare the numbers 98,789,000; 987,890,000; and 89,987,000 in scientific notation, we first convert each number:

1. \( 98,789,000 = 9.8789 \times 10^7 \)
2. \( 987,890,000 = 9.8789 \times 10^8 \)
3. \( 89,987,000 = 8.9987 \times 10^7 \)

Now we compare the numbers:

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

Next, we look at the powers of 10. The number with the lowest power of 10 will have the least value if the digits before the decimal are comparable.

• The numbers \( 9.8789 \times 10^7 \) and \( 8.9987 \times 10^7 \) have the same power of 10 (\( 10^7 \)). Now we compare the coefficients (9.8789 and 8.9987).
• Since \( 8.9987 < 9.8789 \), \( 8.9987 \times 10^7 \) is the smallest.
• \( 9.8789 \times 10^8 \) is clearly greater than both since it has \( 10^8 \).

Thus, the number with the least value is:

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