Choose the appropriate sign for each of the following expressions in the table.(3 points)

Question

< > =
2.14 × 105 ? 2.14 × 103
2.14

×

10
5


?



2.14

×

10
3

8.341 × 10−6 ? 2.15 × 10−2
8.341


×

10
−
6


?


2.15

×

10
−
2

1.98 × 105 ? 8.91 × 105
1.98


×

10
5


?


8.91

×

10
5

Answer 1

To determine the appropriate sign for each expression, we'll compare the numbers on either side of the question mark.

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

   • Convert \( 2.14 × 10^5 \) to standard form: \( 214000 \)
   • Convert \( 2.14 × 10^3 \) to standard form: \( 2140 \)
   • Since \( 214000 > 2140 \), we have: \[ 2.14 \times 10^5 > 2.14 \times 10^3 \]

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

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

3. Comparison of \( 1.98 × 10^5 \) and \( 8.91 × 10^5 \):

   • Convert \( 1.98 × 10^5 \) to standard form: \( 198000 \)
   • Convert \( 8.91 × 10^5 \) to standard form: \( 891000 \)
   • Since \( 198000 < 891000 \), we have: \[ 1.98 \times 10^5 < 8.91 \times 10^5 \]

Now we can summarize the signs for each expression:

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

So the final answers are:

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