Question

The average weight of an elephant is 1.5 x 10^4 pounds. The average weight of a cat is 14 ponds. How much heavier is an elephant than a cat? Express your answer in scientific notation.

Answer 1

To find out how much heavier an elephant is than a cat, we can subtract the average weight of a cat from the average weight of an elephant.

1. The average weight of an elephant is \( 1.5 \times 10^4 \) pounds.
2. The average weight of a cat is \( 14 \) pounds.

First, we express 14 pounds in scientific notation:

\[
14 = 1.4 \times 10^1 \text{ pounds}
\]

Next, we perform the subtraction:

\[
1.5 \times 10^4 - 1.4 \times 10^1
\]

Since we are subtracting numbers in scientific notation, it's helpful to express both terms with the same exponent. We will convert \( 1.4 \times 10^1 \) to have an exponent of 4:

\[
1.4 \times 10^1 = 0.014 \times 10^4
\]

Now we can subtract:

\[
1.5 \times 10^4 - 0.014 \times 10^4 = (1.5 - 0.014) \times 10^4 = 1.486 \times 10^4
\]

Now we can express \( 1.486 \times 10^4 \) in proper scientific notation. Since it's already in the form \( a \times 10^n \) where \( 1 \leq a < 10 \), no adjustment is needed.

Thus, the difference in weight, which tells us how much heavier an elephant is than a cat, is:

\[
\boxed{1.486 \times 10^4} \text{ pounds}
\]