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