Question

The weight of an ant averages about 3×10−6%0D%0A3%0D%0A×%0D%0A10%0D%0A−%0D%0A6%0D%0A kg. There are about 1×1016%0D%0A1%0D%0A×%0D%0A10%0D%0A16%0D%0A 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)%0D%0A kg

Answer 1

no

Answer 2

To find the approximate weight of all the ants in the world, we can multiply the average weight of an ant by the total number of ants.

1. Average weight of one ant = \( 3 \times 10^{-6} \) kg
2. Total number of ants = \( 1 \times 10^{16} \)

Now, we can calculate the total weight of all ants:

\[
\text{Total weight} = (\text{Average weight of one ant}) \times (\text{Total number of ants})
\]

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

Now, we can simplify this:

\[
\text{Total weight} = 3 \times 1 \times 10^{-6 + 16} = 3 \times 10^{10}
\]

Thus, the approximate weight of all the ants in the world is:

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

Answer 3

Let's go through the calculation step-by-step again carefully:

1. **Weight of one ant**:
\[
\text{Weight of one ant} = 3 \times 10^{-6} \text{ kg}
\]

2. **Total number of ants**:
\[
\text{Number of ants} = 1 \times 10^{16}
\]

3. **Total weight of all ants**:
To find this, we multiply the weight of one ant by the total number of ants:
\[
\text{Total weight} = (\text{Weight of one ant}) \times (\text{Number of ants})
\]

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

4. **Perform the multiplication**:
- First, multiply the coefficients:
\[
3 \times 1 = 3
\]
- Then, add the exponents of 10:
\[
-6 + 16 = 10
\]

Therefore:
\[
\text{Total weight} = 3 \times 10^{10} \text{ kg}
\]

So, the total weight of all the ants in the world is indeed:
\[
\boxed{3 \times 10^{10}} \text{ kg}
\]

If there's a specific aspect of the calculation you'd like me to clarify further or if there's any other information you'd like, please let me know!