Choose the appropriate sign for each of the following expressions in the table.
(3 points)
< > =
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
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
Here are the appropriate signs for each expression:
1. 2.14 × 105 < 2.14 × 103
2. -2.14 × 105 < 2.14 × 103
3. -2.14 × 105 > 2.14 × 103
4. -2.14 × 105 = 2.14 × 103
5. 8.341 × 10−6 < 2.15 × 10−2
6. -8.341 × 10−6 < 2.15 × 10−2
7. -8.341 × 10−6 < 2.15 × 10−2
8. -8.341 × 10−6 = 2.15 × 10−2
9. 1.98 × 105 < 8.91 × 105
10. -1.98 × 105 < 8.91 × 105
Note: The " < " sign means "less than," the " > " sign means "greater than," and the " = " sign means "equal to." The "-" sign before a number indicates a negative value.
To determine the appropriate sign for each expression, we need to compare the given numbers. We can compare numbers using the less than (<), greater than (>), or equal to (=) signs.
Let's go through each expression one by one:
1. 2.14 × 10^5 < 2.14 × 10^3
Here, the exponent on 10 is smaller for 2.14 × 10^5 compared to 2.14 × 10^3. So, the value of 2.14 × 10^5 is greater than 2.14 × 10^3. Therefore, the appropriate sign is ">".
2. -2.14 × 10^5 < 2.14 × 10^3
In this expression, we have a negative sign (-) in front of 2.14 × 10^5. Since any negative number is smaller than a positive number, we can say -2.14 × 10^5 is less than 2.14 × 10^3. Therefore, the appropriate sign is "<".
3. -2.14 × 10^5 > 2.14 × 10^3
Similar to the previous expression, the negative sign in front of 2.14 × 10^5 makes it smaller than 2.14 × 10^3. So, -2.14 × 10^5 is less than 2.14 × 10^3. Hence, the appropriate sign is "<".
4. -2.14 × 10^5 = 2.14 × 10^3
In this expression, since the exponent and the magnitude of the numbers are different, -2.14 × 10^5 is not equal to 2.14 × 10^3. Therefore, the appropriate sign is "!=" (not equal to).
5. 8.341 × 10^-6 < 2.15 × 10^-2
Comparing the exponents and the magnitude, we can see that the value of 8.341 × 10^-6 is smaller than 2.15 × 10^-2. So, the appropriate sign is "<".
6. -8.341 × 10^-6 < 2.15 × 10^-2
Similar to expression 2, the negative sign makes -8.341 × 10^-6 smaller than 2.15 × 10^-2. Hence, the appropriate sign is "<".
7. -8.341 × 10^-6 > 2.15 × 10^-2
Again, the negative sign makes -8.341 × 10^-6 smaller than 2.15 × 10^-2. Therefore, the appropriate sign is "<".
8. -8.341 × 10^-6 != 2.15 × 10^-2
As the exponent and the magnitude are different, -8.341 × 10^-6 is not equal to 2.15 × 10^-2. So, the appropriate sign is "!=".
9. 1.98 × 10^5 < 8.91 × 10^5
Comparing the exponents and the magnitude, we find that 1.98 × 10^5 is smaller than 8.91 × 10^5. Thus, the appropriate sign is "<".
10. -1.98 × 10^5 < 8.91 × 10^5
As we have discussed earlier, the negative sign makes -1.98 × 10^5 smaller than 8.91 × 10^5. Therefore, the appropriate sign is "<".
11. -1.98 × 10^5 > 8.91 × 10^5
Here, the negative sign makes -1.98 × 10^5 smaller than 8.91 × 10^5. So, the appropriate sign is "<".
In summary, the appropriate signs for each expression are as follows:
1. 2.14 × 10^5 > 2.14 × 10^3
2. -2.14 × 10^5 < 2.14 × 10^3
3. -2.14 × 10^5 < 2.14 × 10^3
4. -2.14 × 10^5 != 2.14 × 10^3
5. 8.341 × 10^-6 < 2.15 × 10^-2
6. -8.341 × 10^-6 < 2.15 × 10^-2
7. -8.341 × 10^-6 < 2.15 × 10^-2
8. -8.341 × 10^-6 != 2.15 × 10^-2
9. 1.98 × 10^5 < 8.91 × 10^5
10. -1.98 × 10^5 < 8.91 × 10^5
11. -1.98 × 10^5 < 8.91 × 10^5