Multiply in Scientific Notation Practice

Question

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Question
The weight of an ant averages about 3×10−6
kg. There are about 1×1016
ants in the world. What is the approximate weight in kilograms of all the ants in the world? Write the answer in scientific notation.(1 point)
kg
Remaining Attempts : 3
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Answer 1

To find the total weight of all the ants in the world, we need to multiply the average weight of one ant by the total number of ants.

Given:

• Average weight of one ant = \(3 \times 10^{-6}\) kg
• Number of ants = \(1 \times 10^{16}\)

The multiplication in scientific notation follows the formula:

\[ (a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{(m+n)} \]

So we can compute the total weight as follows:

\[ (3 \times 10^{-6}) \times (1 \times 10^{16}) = 3 \times 1 \times 10^{-6 + 16} \]

Calculating the values:

\[ 3 \times 1 = 3 \] \[ -6 + 16 = 10 \]

Thus, the total weight of all the ants is:

\[ 3 \times 10^{10} \text{ kg} \]

So the approximate weight in kilograms of all the ants in the world is:

\[ \boxed{3 \times 10^{10}} \text{ kg} \]