Choose the appropriate sign for each of the following expressions in the table.

(3 points)
< > =
1.98 × 105 ? 8.91 × 105

2.14 × 105 ? 2.14 × 103

8.341 × 10−6 ? 2.15 × 10−2

1 answer

To compare the expressions, we will look at the values associated with each number in scientific notation.

  1. Comparing 1.98 × 10^5 and 8.91 × 10^5:

    • Both expressions have the same power of 10 (10^5).
    • Compare the coefficients: 1.98 and 8.91. Since 1.98 < 8.91, we have:
      • 1.98 × 10^5 < 8.91 × 10^5
  2. Comparing 2.14 × 10^5 and 2.14 × 10^3:

    • The first number has a power of 10^5, while the second has a power of 10^3.
    • The coefficient is the same (2.14), but since 10^5 is greater than 10^3, we have:
      • 2.14 × 10^5 > 2.14 × 10^3
  3. Comparing 8.341 × 10^−6 and 2.15 × 10^−2:

    • The first number has a power of 10^−6, while the second has a power of 10^−2.
    • To compare, we convert both to the same power of 10 (10^−6):
      • 2.15 × 10^−2 = 2.15 × 10^−2 × (10^4/10^4) = 21500 × 10^−6
    • Now compare 8.341 × 10^−6 and 21500 × 10^−6. Since 8.341 < 21500, we have:
      • 8.341 × 10^−6 < 2.15 × 10^−2

Now, summarizing the results in the table format:

| Expression | Sign | |--------------------------------|------| | 1.98 × 10^5 | < | | 2.14 × 10^5 | > | | 8.341 × 10^−6 | < |