- Identify the amount of paper recycled as \(4.6 \times 10^7\) tons and plastic as \(2,600,000\) tons.
- Convert the plastic amount to scientific notation: \(2,600,000 = 2.6 \times 10^6\).
- Align the powers of 10 to perform subtraction: \(2.6 \times 10^6 = 0.26 \times 10^7\).
- Calculate the difference: \(4.6 \times 10^7 - 0.26 \times 10^7 = 4.34 \times 10^7\).
- The final answer is \(\boxed{4.34 \times 10^7}\).
Explanation
- Problem Analysis and Data Preparation
We are given the amount of paper recycled in 2010 as \(4.6 \times 10^7\) tons and the amount of plastic recycled as \(2,600,000\) tons. Our objective is to determine how many more tons of paper were recycled than plastic, which requires us to find the difference between these two quantities. Since the numbers are given in different formats (scientific notation versus standard decimal notation), we must first express both in the same format.
- Converting to Scientific Notation
The amount of plastic recycled is \(2,600,000\) tons. To work with the scientific notation used for the paper, we convert this number by identifying the power of 10:
\[2,600,000 = 2.6 \times 10^6\]
Now we have both quantities in scientific notation:
- Paper: \(4.6 \times 10^7\) tons
- Plastic: \(2.6 \times 10^6\) tons
- Performing the Subtraction
To subtract the two values, it is easiest to express them with the same exponent for the power of 10. We can rewrite the paper recycling amount to match the \(10^7\) power or convert the plastic amount to \(10^7\). It is convenient to express the plastic amount as \(0.26 \times 10^7\):
\[2.6 \times 10^6 = 0.26 \times 10^7\]
Now, we perform the subtraction:
\[(4.6 \times 10^7) - (0.26 \times 10^7) = (4.6 - 0.26) \times 10^7\]
\[4.6 - 0.26 = 4.34\]
Thus, the difference is \(4.34 \times 10^7\) tons.
- Conclusion and Final Result
Comparing our result to the given options, we find that the difference is \(4.34 \times 10^7\) tons, which corresponds to the last option provided. Therefore, in 2010, the amount of paper recycled exceeded the amount of plastic recycled by \(\boxed{4.34 \times 10^7}\) tons.
Examples
Understanding how to compare large quantities expressed in scientific notation is essential for environmental science and data analysis. For instance, if an agency monitors carbon emissions or waste disposal across millions of units, scientists must perform calculations with scientific notation to quickly assess the scale of impact. Mastering these operations allows researchers to effectively quantify environmental changes and communicate data clearly.