Question

The oxygen saturation level of a river is found by dividing the amount of dissolved oxygen the river water currently has per liter by the dissolved oxygen capacity per liter of the water and then converting to a percent. If the river currently has 7.3 milligrams of dis- solved oxygen per liter of water and the dissolved oxygen capacity is 9.8 milligrams per liter, what is the oxygen saturation level, to the nearest percent? A. 34\(\%\) B. 70\(\%\) C. 73\(\%\) D. 74\(\%\) E. 98\(\%\)

Short answer

Round your answer to the nearest percent. A) 68% B) 70% C) 72% D) 74% E) 76% Answer: D) 74%

Step-by-step solution

Calculate the ratio of dissolved oxygen to capacity

Divide the amount of dissolved oxygen (7.3 mg/L) by the dissolved oxygen capacity (9.8 mg/L): Ratio = \(\frac{7.3}{9.8}\)

Convert the ratio to a percentage

Multiply the ratio by 100 to convert it to a percentage: Percentage = Ratio × 100 = \(\frac{7.3}{9.8} \times 100\)

Calculate the oxygen saturation percentage

Calculate the result of the expression: Percentage = \(\frac{7.3}{9.8} \times 100 \approx 74.49 \)

Round the percentage to the nearest percent

Since we are asked for the oxygen saturation level to the nearest percent, we round the result from Step 3: Oxygen saturation level ≈ 74\(\%\)

Choose the correct answer

The answer that matches our result is option D (74\(\%\)).

Key concepts

Dissolved Oxygen

Understanding the concept of dissolved oxygen (DO) is crucial for interpreting the health of aquatic ecosystems, including rivers, lakes, and oceans. Dissolved oxygen refers to the amount of oxygen that is present in the water and available for aquatic organisms to use. It is important for the survival of fish, plankton, and various microorganisms which rely on it for respiration, similar to how land animals depend on atmospheric oxygen.

The level of dissolved oxygen in a body of water can be influenced by several factors, including temperature, pressure, salinity, and the presence of plants and algae. For example, cold water holds more dissolved oxygen than warm water. The oxygen saturation level, therefore, is a measure that reflects the percentage of oxygen present compared to the maximum amount the water can hold at a given temperature and pressure. It's essential for determining how habitable the water is for aquatic life.

Ratio and Proportion

Ratio and proportion are foundational concepts in many scientific calculations and everyday situations. A ratio is a relationship between two numbers indicating how many times the first number contains the second. In calculating the oxygen saturation level, the amount of dissolved oxygen per liter is compared to the dissolved oxygen capacity per liter, effectively creating a ratio.

Proportion, on the other hand, signifies that two ratios are equal. When we calculate oxygen saturation, we are actually finding a proportion: the dissolved oxygen to its capacity is equivalent to the unknown saturation level to 100 percent. Understanding how to manipulate ratios and proportions is essential for converting these relationships into accurate and meaningful percentages.

Percentage Conversion

Percentage conversion is a method to express a ratio as a fraction of 100, and it's very common in analyzing scientific data because it allows for an easy comparison. Moving from a decimal or ratio to a percentage can be done simply by multiplying by 100. This conversion is utilized when calculating oxygen saturation levels from the determined ratio of dissolved oxygen to its capacity. It is essential to represent the information in a percentage as it gives a clear picture of how saturated the water is with oxygen; for instance, a 100% saturation means the water is fully saturated with oxygen under the existing environmental conditions, and lower percentages indicate less dissolved oxygen.

Scientific Measurement

Scientific measurement involves the collection and quantification of data in a standardized manner, enabling consistency and reliability. It is crucial in experiments, assessments, and, as illustrated in our problem, environmental monitoring. In measuring dissolved oxygen, the amount is often recorded in milligrams per liter (mg/L), which is a unit of concentration. It's a precise way to represent how much of a substance exists within a particular volume of liquid.

Accuracy in scientific measurement is vital as it impacts the reliability of data and subsequent conclusions. Hence, measurements should always be taken carefully, and the use of proper units of measure is essential. In making environmental assessments, such as determining oxygen saturation levels, precise measurements allow accurate calculations that are critical for understanding ecological conditions and making informed decisions.