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

Question

(3 points)
< > =
1.98 × 10^5 ? 8.91 × 10^5

8.341 × 10^−6 ? 2.15 × 10^−2

2.14 × 10^5 ? 2.14 × 10^3

Answer 1

To compare the expressions, we need to analyze their values:

1. Comparison of \( 1.98 \times 10^5 \) and \( 8.91 \times 10^5 \):

   • \( 1.98 \times 10^5 = 198000 \)
   • \( 8.91 \times 10^5 = 891000 \)
   • Since \( 198000 < 891000 \), we have: \[ 1.98 \times 10^5 < 8.91 \times 10^5 \]

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

   • \( 8.341 \times 10^{-6} = 0.000008341 \)
   • \( 2.15 \times 10^{-2} = 0.0215 \)
   • Since \( 0.000008341 < 0.0215 \), we have: \[ 8.341 \times 10^{-6} < 2.15 \times 10^{-2} \]

3. Comparison of \( 2.14 \times 10^5 \) and \( 2.14 \times 10^3 \):

   • \( 2.14 \times 10^5 = 214000 \)
   • \( 2.14 \times 10^3 = 2140 \)
   • Since \( 214000 > 2140 \), we have: \[ 2.14 \times 10^5 > 2.14 \times 10^3 \]

Putting this all together, we can fill in the table:

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

So, the signs you need are:

1. \( < \)
2. \( < \)
3. \( > \)