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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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: \[ \boxed{2 \times 10^{9}} \]

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The total weight of about \( 2 \times 10^{9} \) ants equals the weight of an average-sized elephant.
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