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
Here are the appropriate signs for each expression:
1.98 × 105 < 8.91 × 105 (less than)
- 1.98 × 105 < 8.91 × 105 (less than)
- 1.98 × 105 > 8.91 × 105 (greater than)
- 1.98 × 105 = 8.91 × 105 (equal to)
2.14 × 105 = 2.14 × 103 (equal to)
- 2.14 × 105 > 2.14 × 103 (greater than)
- 2.14 × 105 > 2.14 × 103 (greater than)
- 2.14 × 105 = 2.14 × 103 (equal to)
8.341 × 10−6 < 2.15 × 10−2 (less than)
To determine the appropriate sign for each expression, we need to compare the values of the numbers given.
1.98 × 10^5 ? 8.91 × 10^5
To compare these values, we look at the exponents first. Both numbers have the same exponent (5), so we focus on the coefficient. 1.98 is less than 8.91, so the appropriate sign is "<" (less than).
-1.98 × 10^5 ? 8.91 × 10^5
Similar to the previous expression, we compare the values after looking at the exponents. In this case, -1.98 is a negative number, while 8.91 is positive. Negative numbers are always considered smaller than positive numbers, so the appropriate sign is "<" (less than).
-1.98 × 10^5 ? 8.91 × 10^5
Again, we compare the values after considering the exponents. Since -1.98 is a negative number and 8.91 is positive, the negative number is considered smaller, and the appropriate sign is "<" (less than).
= -1.98 × 10^5 ? 8.91 × 10^5
Once more, we compare the values after examining the exponents. Since -1.98 is a negative number and 8.91 is positive, they are not equal. Therefore, the appropriate sign is "≠" (not equal).
2.14 × 10^5 ? 2.14 × 10^3
We compare the values after checking the exponents. Both numbers have the same exponent (5), so we focus on the coefficient. 2.14 is equal to 2.14, so the appropriate sign is "=" (equal).
-2.14 × 10^5 ? 2.14 × 10^3
Similar to the previous expression, we compare the values after considering the exponents. In this case, -2.14 is a negative number, while 2.14 is positive. Negative numbers are always considered smaller than positive numbers, so the appropriate sign is "<" (less than).
-2.14 × 10^5 ? 2.14 × 10^3
Again, we compare the values after examining the exponents. Since -2.14 is a negative number and 2.14 is positive, the negative number is considered smaller, and the appropriate sign is "<" (less than).
= -2.14 × 10^5 ? 2.14 × 10^3
Once more, we compare the values after checking the exponents. Since -2.14 is a negative number and 2.14 is positive, they are not equal. Therefore, the appropriate sign is "≠" (not equal).
8.341 × 10^-6 ? 2.15 × 10^-2
To compare these values, we look at the exponents first. Both numbers have a negative exponent. Since the exponent -2 is greater than -6, the magnitude of the number with the greater exponent is greater. Therefore, the appropriate sign is ">" (greater than).
I hope this explanation helps!
To determine the appropriate signs for the given expressions, we need to compare the values on both sides of the expressions. Here are the signs for each expression:
1.98 × 105 ? 8.91 × 105:
This expression can be rewritten as "1.98 × 105 < 8.91 × 105", which means 1.98 × 105 is less than 8.91 × 105. Therefore, the appropriate sign is "<" (less than).
-1.98 × 105 ? 8.91 × 105:
This expression can be rewritten as "-1.98 × 105 < 8.91 × 105", which means -1.98 × 105 is less than 8.91 × 105. Therefore, the appropriate sign is "<" (less than).
-1.98 × 105 ? 8.91 × 105:
This expression can be rewritten as "-1.98 × 105 > 8.91 × 105", which means -1.98 × 105 is greater than 8.91 × 105. Therefore, the appropriate sign is ">" (greater than).
-1.98 × 105 ? 8.91 × 105:
This expression can be rewritten as "-1.98 × 105 = 8.91 × 105", which means -1.98 × 105 is equal to 8.91 × 105. Therefore, the appropriate sign is "=" (equal to).
2.14 × 105 ? 2.14 × 103:
This expression can be rewritten as "2.14 × 105 > 2.14 × 103", which means 2.14 × 105 is greater than 2.14 × 103. Therefore, the appropriate sign is ">" (greater than).
-2.14 × 105 ? 2.14 × 103:
This expression can be rewritten as "-2.14 × 105 < 2.14 × 103", which means -2.14 × 105 is less than 2.14 × 103. Therefore, the appropriate sign is "<" (less than).
-2.14 × 105 ? 2.14 × 103:
This expression can be rewritten as "-2.14 × 105 > 2.14 × 103", which means -2.14 × 105 is greater than 2.14 × 103. Therefore, the appropriate sign is ">" (greater than).
-2.14 × 105 ? 2.14 × 103:
This expression can be rewritten as "-2.14 × 105 = 2.14 × 103", which means -2.14 × 105 is equal to 2.14 × 103. Therefore, the appropriate sign is "=" (equal to).
8.341 × 10−6 ? 2.15 × 10−2:
This expression can be rewritten as "8.341 × 10−6 < 2.15 × 10−2", which means 8.341 × 10−6 is less than 2.15 × 10−2. Therefore, the appropriate sign is "<" (less than).
Here is the summary of the appropriate signs for each expression:
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: <