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10. The average weight of an elephant is 1.15 * 10 ^ 4 pounds. The average weight of a cat is 14 pounds. How much heavier is an elephant than a cat? Express your answer in scientific notation.
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To find out how much heavier an elephant is than a cat, we need to subtract the weight of a cat from the weight of an elephant.
Elephant weight = 1.15 * 10 ^ 4 pounds
Cat weight = 14 pounds
Hence, the difference in weight is:
1.15 * 10 ^ 4 pounds - 14 pounds
To subtract these numbers, we need to convert the weight of the cat to scientific notation:
14 pounds = 1.4 * 10 ^ 1 pounds
Now we can subtract:
1.15 * 10 ^ 4 pounds - 1.4 * 10 ^ 1 pounds
To subtract numbers in scientific notation, we need to have the same exponents (powers of 10). Let's convert the weight of the cat to have an exponent of 4:
1.4 * 10 ^ 1 pounds = 0.14 * 10 ^ 4 pounds
Now we can subtract:
1.15 * 10 ^ 4 pounds - 0.14 * 10 ^ 4 pounds
To subtract these numbers, we subtract the coefficients (1.15 - 0.14) and leave the exponent the same:
1.01 * 10 ^ 4 pounds
Therefore, an elephant is 1.01 * 10 ^ 4 pounds heavier than a cat.
To find out how much heavier an elephant is than a cat, we can subtract the weight of the cat from the weight of the elephant.
The weight of an elephant is 1.15 * 10^4 pounds.
The weight of a cat is 14 pounds.
Subtracting the weight of the cat from the weight of the elephant gives us:
1.15 * 10^4 pounds - 14 pounds
To subtract these values, we need to express them in the same units.
14 pounds can be written as 1.4 * 10^1 pounds (since 14 can be written as 1.4 * 10^1)
Now we can subtract:
1.15 * 10^4 pounds - 1.4 * 10^1 pounds
To subtract these values, we need to have the same exponent.
1.4 * 10^1 pounds can be written as 1.4 * 10^4 pounds (by adding the exponent by 3)
Now we can subtract:
1.15 * 10^4 pounds - 1.4 * 10^4 pounds
Subtracting the values:
1.15 - 1.4 = -0.25
The result is negative because the elephant is lighter than the cat.
So, the elephant is 0.25 * 10^4 pounds lighter than the cat.
Expressing it in scientific notation, we can write:
-0.25 * 10^4 pounds or -2.5 * 10^3 pounds
Therefore, the elephant is 2.5 * 10^3 pounds lighter than the cat.
To determine how much heavier an elephant is than a cat, we need to subtract the weight of a cat from the weight of an elephant.
Weight of an elephant = 1.15 * 10^4 pounds
Weight of a cat = 14 pounds
Subtracting the weight of a cat from the weight of an elephant:
1.15 * 10^4 pounds - 14 pounds
To subtract the weights, we need to convert both weights to the same exponent in scientific notation. To convert the weight of a cat to scientific notation, it is already in scientific notation with an exponent of 10^0.
Now we need to express the weight of a cat in scientific notation with the same exponent as the weight of an elephant, which is 10^4.
To do so, we can write 14 pounds as 1.4 * 10^1 pounds.
Now we can proceed with the subtraction:
1.15 * 10^4 pounds - 1.4 * 10^1 pounds = 1.15 * 10^4 pounds - 1.4 * 10^1 pounds
To subtract the weights, we should subtract the coefficients (1.15 - 1.4) and keep the exponents unchanged:
= (1.15 - 1.4) * 10^4 pounds
= (-0.25) * 10^4 pounds
Finally, we can express the result in scientific notation:
= -2.5 * 10^(-1) * 10^4 pounds
= -2.5 * 10^(-1 + 4) pounds
= -2.5 * 10^3 pounds
Therefore, an elephant is -2.5 * 10^3 pounds heavier than a cat.