Sure, let's solve this problem step by step to find the number of persons per square kilometer given the population and the area of the world.
1. Understand the Given Values:
- The world population is approximately [tex]\(5 \times 10^9\)[/tex] people.
- The total area of the world is [tex]\(4 \times 10^{11}\)[/tex] square kilometers.
2. The Formula to Use:
To find the number of persons per square kilometer, you need to divide the total population by the total area. The formula is:
[tex]\[
\text{Persons per sq km} = \frac{\text{Total Population}}{\text{Total Area}}
\][/tex]
3. Substitute the Given Values into the Formula:
Here, the total population is [tex]\(5 \times 10^9\)[/tex] and the total area is [tex]\(4 \times 10^{11}\)[/tex]. Substituting these values into the formula gives:
[tex]\[
\text{Persons per sq km} = \frac{5 \times 10^9}{4 \times 10^{11}}
\][/tex]
4. Simplify the Expression:
To simplify,
[tex]\[
\frac{5 \times 10^9}{4 \times 10^{11}} = \frac{5}{4} \times \frac{10^9}{10^{11}}
\][/tex]
5. Calculate the Powers of Ten:
When dividing exponents with the same base, subtract the exponents:
[tex]\[
\frac{10^9}{10^{11}} = 10^{9-11} = 10^{-2}
\][/tex]
6. Combine the Results:
Now, multiply the simplified fraction with the power of ten:
[tex]\[
\frac{5}{4} \times 10^{-2} = 1.25 \times 10^{-2}
\][/tex]
7. Convert to Decimal Form:
[tex]\[
1.25 \times 10^{-2} = 0.0125
\][/tex]
8. Result:
So, the number of persons per square kilometer is [tex]\(0.0125\)[/tex].
To summarize, given the world population of [tex]\(5 \times 10^9\)[/tex] and an area of [tex]\(4 \times 10^{11}\)[/tex] square kilometers, the number of persons per square kilometer is [tex]\(0.0125\)[/tex].
