Verified Answer :
- Identify the given values: total aquarium volume is \(1 \times 10^5\) gallons and each neon tetra requires \(1.25\) gallons.
- Determine the total number of tetras by dividing total volume by volume per tetra: \(N = \frac{1 \times 10^5}{1.25} = 80,000\).
- Convert the result into scientific notation by shifting the decimal point to express the number as a factor multiplied by a power of 10.
- Final answer: \(\boxed{8 \times 10^4}\).
Explanation
- Problem Analysis
To determine the maximum number of neon tetras that can be housed in the aquarium, we need to divide the total volume of water available by the volume of water required for each individual neon tetra. We are given that each neon tetra requires \(1.25\) gallons of water, and the aquarium has a total capacity of \(1 \times 10^5\) gallons. Let \(N\) represent the total number of tetras, so the relationship is given by \(N = \frac{1 \times 10^5}{1.25}\).
- Calculation of Total Tetras
We perform the division of the total capacity by the volume per tetra:
\[N = \frac{100,000}{1.25}\]
To simplify this calculation, we can write \(1.25\) as a fraction: \(1.25 = \frac{5}{4}\). Therefore, the expression becomes:
\[N = 100,000 \div \frac{5}{4} = 100,000 \times \frac{4}{5}\]
Dividing \(100,000\) by \(5\) gives \(20,000\), and multiplying that result by \(4\) yields:
\[N = 20,000 \times 4 = 80,000\]
- Conclusion and Scientific Notation Representation
The result of our calculation is \(80,000\). To express this number in scientific notation, we write it as a product of a number between \(1\) and \(10\) and a power of \(10\). Moving the decimal point in \(80,000\) four places to the left gives us \(8.0\). Thus, the number of neon tetras in scientific notation is:
\[80,000 = 8 \times 10^4\]
So, the aquarium can house \(8 \times 10^4\) neon tetras.
Examples
In real life, understanding how to calculate population capacity within a specific resource limit is vital for fields like biology, resource management, and city planning. For instance, an urban planner might use similar calculations to determine how many people can comfortably inhabit a given space while ensuring that utilities like water and electricity are adequately distributed. By converting large, unwieldy numbers into scientific notation, as shown in this problem, professionals can more easily manage, compare, and communicate vast quantities of data.