Choose the appropriate sign for each of the following expressions in the table.
(3 points)
< > =
1.98 × 105 ? 8.91 × 105
< – 1.98 × 105 ? 8.91 × 105
> – 1.98 × 105 ? 8.91 × 105
= – 1.98 × 105 ? 8.91 × 105
2.14 × 105 ? 2.14 × 103
< – 2.14 × 105 ? 2.14 × 103
> – 2.14 × 105 ? 2.14 × 103
= – 2.14 × 105 ? 2.14 × 103
8.341 × 10−6 ? 2.15 × 10−2
< – 8.341 × 10−6 ? 2.15 × 10−2
> – 8.341 × 10−6 ? 2.15 × 10−2
= – 8.341 × 10−6 ? 2.15 × 10−2
1.98 × 105 > 8.91 × 105
< – 1.98 × 105 < 8.91 × 105
> – 1.98 × 105 < 8.91 × 105
= – 1.98 × 105 < 8.91 × 105
2.14 × 105 = 2.14 × 103
< – 2.14 × 105 > 2.14 × 103
> – 2.14 × 105 > 2.14 × 103
= – 2.14 × 105 > 2.14 × 103
8.341 × 10−6 < 2.15 × 10−2
< – 8.341 × 10−6 < 2.15 × 10−2
> – 8.341 × 10−6 < 2.15 × 10−2
= – 8.341 × 10−6 < 2.15 × 10−2
Here are the appropriate signs for each of the expressions:
1.98 × 10^5 < 8.91 × 10^5
-1.98 × 10^5 < 8.91 × 10^5
-1.98 × 10^5 > 8.91 × 10^5
-1.98 × 10^5 = 8.91 × 10^5
2.14 × 10^5 = 2.14 × 10^3
-2.14 × 10^5 < 2.14 × 10^3
-2.14 × 10^5 > 2.14 × 10^3
-2.14 × 10^5 = 2.14 × 10^3
8.341 × 10^-6 < 2.15 × 10^-2
-8.341 × 10^-6 < 2.15 × 10^-2
-8.341 × 10^-6 > 2.15 × 10^-2
-8.341 × 10^-6 = 2.15 × 10^-2
To determine the appropriate sign for each expression in the table, we need to compare the given numbers and consider their values.
For the first set of expressions:
1.98 × 105 ? 8.91 × 105
We can see that 1.98 × 105 is less than 8.91 × 105, so the sign < is appropriate.
< – 1.98 × 105 ? 8.91 × 105
Here, we have -1.98 × 105 on the left, which is less than 8.91 × 105. Therefore, the sign < is also appropriate.
> – 1.98 × 105 ? 8.91 × 105
Since -1.98 × 105 is less than 8.91 × 105, the sign > is appropriate.
= – 1.98 × 105 ? 8.91 × 105
In this case, -1.98 × 105 is not equal to 8.91 × 105, so the sign = is not appropriate.
Moving on to the second set of expressions:
2.14 × 105 ? 2.14 × 103
The two values are equal, so the sign = is appropriate.
< – 2.14 × 105 ? 2.14 × 103
Since the left side is negative (-2.14 × 105) and the right side is positive (2.14 × 103), the sign < is appropriate.
> – 2.14 × 105 ? 2.14 × 103
Similarly, the left side is still negative and the right side is positive, so the sign > is appropriate.
= – 2.14 × 105 ? 2.14 × 103
Again, the left side is negative and the right side is positive, resulting in the sign = being appropriate.
Lastly, for the third set of expressions:
8.341 × 10−6 ? 2.15 × 10−2
The left side is smaller than the right side, so the sign < is appropriate.
< – 8.341 × 10−6 ? 2.15 × 10−2
With the negative value on the left and the positive one on the right, the sign < is appropriate.
> – 8.341 × 10−6 ? 2.15 × 10−2
Since the left side is negative and the right side is positive, the sign > is appropriate.
= – 8.341 × 10−6 ? 2.15 × 10−2
Again, we have a negative value on the left and a positive one on the right, resulting in the sign = being appropriate.
Therefore, the appropriate signs for the expressions are as follows:
1.98 × 105 ? 8.91 × 105: <
< – 1.98 × 105 ? 8.91 × 105: <
> – 1.98 × 105 ? 8.91 × 105: >
= – 1.98 × 105 ? 8.91 × 105: not =
2.14 × 105 ? 2.14 × 103: =
< – 2.14 × 105 ? 2.14 × 103: <
> – 2.14 × 105 ? 2.14 × 103: >
= – 2.14 × 105 ? 2.14 × 103: not =
8.341 × 10−6 ? 2.15 × 10−2: <
< – 8.341 × 10−6 ? 2.15 × 10−2: <
> – 8.341 × 10−6 ? 2.15 × 10−2: >
= – 8.341 × 10−6 ? 2.15 × 10−2: not =