Let's determine how many average-sized ants would be required to wrap around the Earth.
1. Let's first understand the lengths we are dealing with:
- The length of one ant is approximately [tex]\(4 \times 10^{-3}\)[/tex] meters.
- The circumference of the Earth is approximately [tex]\(4 \times 10^7\)[/tex] meters.
2. To find out how many ants are needed to wrap around the Earth, we need to divide the circumference of the Earth by the length of one ant. Mathematically, this can be expressed as:
[tex]\[
\text{Number of ants} = \frac{\text{Circumference of the Earth}}{\text{Length of one ant}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Number of ants} = \frac{4 \times 10^7 \text{ meters}}{4 \times 10^{-3} \text{ meters}}
\][/tex]
3. Simplify the division:
[tex]\[
\frac{4 \times 10^7}{4 \times 10^{-3}} = \left( \frac{4}{4} \right) \times \left( 10^7 \times 10^3 \right)
\][/tex]
4. Simplify the fractions and exponents:
[tex]\[
1 \times 10^{7 + 3} = 1 \times 10^{10}
\][/tex]
5. Combining the calculation:
[tex]\[
1 \times 10^{10} = 10^{10}
\][/tex]
6. Converting [tex]\(10^{10}\)[/tex] to standard form gives us:
[tex]\[
10,000,000,000
\][/tex]
Thus, it would take ten billion ants to wrap around the Earth.
