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. $>$