Riley Ayala
07/21/2024 · Middle School
(4) An ant weighs about \( 4 \times 10^{-3} \) gram. An average-sized elephant weighs \( 8 \times 10^{6} \) grams. (4) The total weight of about how many ants equals the weight of an average-sized elephant?
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Step-by-step Solution
To find out how many ants weigh the same as an average-sized elephant, we can divide the weight of the elephant by the weight of one ant.
The weight of one ant is \( 4 \times 10^{-3} \) grams, and the weight of an average-sized elephant is \( 8 \times 10^{6} \) grams.
We can set up the calculation as follows:
\[
\text{Number of ants} = \frac{\text{Weight of elephant}}{\text{Weight of one ant}} = \frac{8 \times 10^{6} \text{ grams}}{4 \times 10^{-3} \text{ grams}}
\]
Now, we can simplify this:
\[
\text{Number of ants} = \frac{8}{4} \times \frac{10^{6}}{10^{-3}} = 2 \times 10^{6} \times 10^{3}
\]
Using the property of exponents \( a^m \times a^n = a^{m+n} \):
\[
\text{Number of ants} = 2 \times 10^{6 + 3} = 2 \times 10^{9}
\]
Thus, the total weight of about \( 2 \times 10^{9} \) ants equals the weight of an average-sized elephant.
So, the answer is:
\[
\boxed{2 \times 10^{9}}
\]
Quick Answer
The total weight of about \( 2 \times 10^{9} \) ants equals the weight of an average-sized elephant.
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