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.

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.