- Identify the variables: grant amount \(G = 1.925 \times 10^6\) and cost per lunch \(C = 2.75\).
- Divide the grant by the cost per lunch: \(\frac{1.925 \times 10^6}{2.75} = 0.7 \times 10^6\).
- Convert the result to scientific notation: \(0.7 \times 10^6 = 7 \times 10^5\).
- Select the matching option: \(\boxed{7 \times 10^5}\).
Explanation
- Analysis of the Problem
The problem asks us to calculate the total number of senior lunches that can be funded by a grant of \(\$1.925 \times 10^6\) dollars, given that each lunch costs \(\$2.75\) dollars. To find the total number of lunches, we must divide the total grant amount by the cost per lunch. Let \(G = 1.925 \times 10^6\) be the grant amount and \(C = 2.75\) be the cost per lunch. We need to calculate \(L = \frac{G}{C}\).
- Calculation of the Number of Lunches
To perform the division \(\frac{1.925 \times 10^6}{2.75}\), we can separate the calculation into the division of the coefficient and the power of 10. We have:
\[L = \left(\frac{1.925}{2.75}\right) \times 10^6\]
Performing the division \(\frac{1.925}{2.75}\) yields \(0.7\).
Therefore, we have \(L = 0.7 \times 10^6\).
- Converting to Scientific Notation and Final Answer
Scientific notation requires the coefficient to be between 1 and 10. Currently, we have \(0.7 \times 10^6\). To convert this to proper scientific notation, we shift the decimal point one place to the right, which increases the value of the coefficient but decreases the power of 10 by 1:
\[0.7 \times 10^6 = 7 \times 10^{-1} \times 10^6 = 7 \times 10^5\]
Thus, the grant can provide \(7 \times 10^5\) senior lunches. Comparing this result with the given options, it corresponds to the second choice.
Examples
Understanding how to perform calculations with scientific notation is essential in fields like finance and science where very large or very small numbers are common. For example, if a government allocates a budget for public infrastructure projects or large-scale health initiatives, they often express these amounts in scientific notation to make them easier to handle and compare. Mastering this skill allows you to quickly estimate the reach of resources, such as determining how many individuals can be supported by a specific budget, just as we did with the senior lunch program.