Choose the appropriate sign for each of the following expressions in the table. (3 points) < > = 8.341 × 10−6 ? 2.15 × 10−2 2.14 × 105 ? 2.14 × 103 1.98 × 105 ? 8.91 × 105

Answer 1

To determine the appropriate signs (<, >, =) for each of the given expressions, we will compare the numbers in standard form.

1. Compare \(8.341 \times 10^{-6}\) and \(2.15 \times 10^{-2}\):

   • \(8.341 \times 10^{-6} = 0.000008341\)
   • \(2.15 \times 10^{-2} = 0.0215\)
   • Conclusion: \(8.341 \times 10^{-6} < 2.15 \times 10^{-2}\)

2. Compare \(2.14 \times 10^{5}\) and \(2.14 \times 10^{3}\):

   • \(2.14 \times 10^{5} = 214000\)
   • \(2.14 \times 10^{3} = 2140\)
   • Conclusion: \(2.14 \times 10^{5} > 2.14 \times 10^{3}\)

3. Compare \(1.98 \times 10^{5}\) and \(8.91 \times 10^{5}\):

   • \(1.98 \times 10^{5} = 198000\)
   • \(8.91 \times 10^{5} = 891000\)
   • Conclusion: \(1.98 \times 10^{5} < 8.91 \times 10^{5}\)

Putting it all together, the results are:

1. \(8.341 \times 10^{-6} < 2.15 \times 10^{-2}\)
2. \(2.14 \times 10^{5} > 2.14 \times 10^{3}\)
3. \(1.98 \times 10^{5} < 8.91 \times 10^{5}\)

Here’s the final answer in table format:

| Expression | Sign | |-----------------------------------|-------| | \(8.341 \times 10^{-6} ? 2.15 \times 10^{-2}\) | < | | \(2.14 \times 10^{5} ? 2.14 \times 10^{3}\) | > | | \(1.98 \times 10^{5} ? 8.91 \times 10^{5}\) | < |