Question

Choose the appropriate sign for each of the following expressions in the table.(3 points)< > = 1.98 × 10^5 ? 8.91 × 10^5 2.14 × 10^5 ? 2.14 × 10^3 8.341 × 10^−6 ? 2.15 × 10^−2

Answer 1

To compare the numbers in scientific notation, we need to look at both the coefficients and the powers of 10.

1. **1.98 × 10^5 ? 8.91 × 10^5**
- The exponents are both 5, so we only need to compare the coefficients: 1.98 and 8.91.
- Since 1.98 < 8.91, the sign is **<**.

2. **2.14 × 10^5 ? 2.14 × 10^3**
- Here, the first term's exponent is 5 and the second term's exponent is 3. Since 10^5 is much larger than 10^3, even though the coefficients are equal, the first number is greater.
- The sign is **>**.

3. **8.341 × 10^−6 ? 2.15 × 10^−2**
- In this case, we need to compare the powers of 10. The first term has an exponent of -6, while the second has -2. Since -6 is less than -2, 10^−6 is smaller than 10^−2.
- Thus, we can see that 8.341 × 10^−6 is smaller than 2.15 × 10^−2.
- The sign is **<**.

Putting it all together, we have:

1. 1.98 × 10^5 < 8.91 × 10^5
2. 2.14 × 10^5 > 2.14 × 10^3
3. 8.341 × 10^−6 < 2.15 × 10^−2