- The total area is obtained by summing the areas of the park and the forest: \(1.42 \times 10^6 + 1.2 \times 10^6\).
- Using the distributive property, factor out the common power of 10: \((1.42 + 1.2) \times 10^6\).
- Perform the arithmetic to find the sum: \(2.62 \times 10^6\).
- The total combined area is \(\boxed{2.62 \times 10^6}\) acres.
Explanation
- Problem Analysis
The problem asks for the combined area of a national park and a national forest. We are given the area of the national park as \(1.42 \times 10^6\) acres and the area of the national forest as \(1.2 \times 10^6\) acres. Our goal is to find the total combined area, expressed in scientific notation.
- Combining the Areas
To calculate the total area, we must sum the two given values:
\[A_{total} = (1.42 \times 10^6) + (1.2 \times 10^6).\]
Since both numbers are expressed in scientific notation with the same power of 10 (\(10^6\)), we can factor out the common term to simplify the addition:
\[A_{total} = (1.42 + 1.2) \times 10^6.\]
- Calculation and Result
Now, we perform the addition of the numerical coefficients:
\[1.42 + 1.2 = 2.62.\]
Therefore, the total area is:
\[A_{total} = 2.62 \times 10^6.\]
This matches the first option provided in the problem description.
Examples
Scientific notation is a highly efficient way to express very large or very small numbers, which is common in fields like astronomy, biology, and environmental science. For instance, if you are tracking the total population of migratory birds across several large nature reserves or calculating the total storage capacity of data centers worldwide in gigabytes, you use scientific notation to handle these massive figures without dealing with long strings of zeros. This skill makes comparing and operating with large datasets much simpler and less prone to errors.