there are 6.54 million people in Indiana. The area of Indiana is 36,185 square miles. Write each number in scientific notation. Use scientific notation to calculate Indiana’s people per square miles. This is called the population density. Write the standard form, rounded to a whole number. Write a sentence using your answer from part b to explain the meaning of Indiana’s population density.
there are 6.54 million people in Indiana. The area of Indiana is 36,185 square miles.ÂÂ
Write each number in scientific notation.
Use scientific notation to calculate Indiana’s people per square miles. This is called the population density. Write the standard form, rounded to a whole number.
Write a sentence using your answer from part b to explain the meaning of Indiana’s population density.
The Correct Answer and Explanation is :
Step 1: Write the numbers in scientific notation.
- Population of Indiana: 6.54 million people is 6.54 × 10^6 in scientific notation.
- Area of Indiana: 36,185 square miles is 3.6185 × 10^4 in scientific notation.
Step 2: Calculate the population density using scientific notation.
Population density is the number of people per square mile. To calculate it, we divide the population by the area.
[
\text{Population Density} = \frac{6.54 \times 10^6}{3.6185 \times 10^4}
]
This gives us:
[
\text{Population Density} = \frac{6.54}{3.6185} \times 10^{6-4} = 1.808 \times 10^2
]
This simplifies to:
[
\text{Population Density} = 180.8 \text{ people per square mile}
]
Step 3: Round to the nearest whole number.
Rounding 180.8 to the nearest whole number gives us 181 people per square mile.
Step 4: Write a sentence to explain the meaning of Indiana’s population density.
Indiana’s population density of 181 people per square mile means that, on average, there are 181 people living in each square mile of land in the state. This number reflects how crowded or spacious the state is in terms of its population relative to its area.
Explanation (300 words):
Population density is a key metric used to understand the distribution of people across a given area. It provides insight into how crowded or spacious a region is, which can have implications for resource allocation, urban planning, transportation, and even the overall quality of life. In the case of Indiana, with a population of 6.54 million people and an area of 36,185 square miles, the population density helps give a snapshot of how many people live in each square mile.
Using scientific notation simplifies the calculations, especially with large numbers. By writing the population and area in scientific notation, we can handle the division more easily, and it ensures accuracy in our calculations. After dividing the two quantities, we find that Indiana’s population density is approximately 181 people per square mile. This means that, for every square mile of land in Indiana, there are 181 people living there on average.
This value tells us that Indiana is not as densely populated as major metropolitan areas, but it still has a moderate population density. Areas with higher population densities tend to have more urban characteristics, like crowded cities and more infrastructure, while regions with lower population densities are often more rural. Understanding population density helps policymakers, businesses, and citizens make informed decisions about where to live, where to build, and how to manage resources effectively. In Indiana’s case, the population density suggests that there’s enough space for growth while still maintaining a vibrant population throughout the state.