Question

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