Data Handling: Rates, Ratios and Proportions

A research team is analyzing the growth rate of a bacterial colony under different nutrient conditions. Which data handling method would be most effective for comparing the growth rates across these conditions?

An investor is evaluating the performance of two stocks. Stock A increased from $50 to $60 in one year, while Stock B decreased from $80 to $70 in the same period. How should the investor interpret these changes?

A chef is scaling a recipe that originally makes 6 servings to now make 15 servings. The original recipe calls for 2 cups of flour. How should the chef determine the new amount of flour needed while maintaining the recipe's proportions?

A scientist measures the size of a cell as 0.0000025 meters. Which number format would be most appropriate and practical for scientific communication and publication?

A car travels 300 kilometers in 4 hours. What does the rate, calculated as kilometers per hour, primarily represent in this scenario?

In a study involving population estimates, a researcher calculates the population of a town to be 15,753. For a report aimed at a general audience, how should the researcher present this number to enhance clarity?

A company's revenue increased from $2.5 million to $3.2 million in one year. Which of the following provides the most accurate analysis of this change?

An urban planner is designing a new park and wants to maintain a consistent ratio of green space to paved areas as seen in a successful park design. If the existing park has 800 square meters of green space and 200 square meters of paved areas, what aspect is most critical for the urban planner to consider?

A laboratory is analyzing a chemical reaction that produces 0.000045 grams of a substance. What would be the most appropriate way to express this quantity in a scientific publication?

An athlete runs 10 kilometers in 45 minutes. What does calculating the rate of kilometers per hour primarily tell us about the athlete's performance?

A survey records the average household income in a town as $62,789. When presenting this information to the public, how should it be rounded to best communicate the data?

A company's profits decreased from $8 million to $6.4 million. Which calculation correctly reflects the percentage change in profits?

An architect is designing a scale model of a building, where 1 inch on the model represents 8 feet in the actual building. If the building's planned height is 120 feet, what height should the architect use for the model?

A computer program calculates a result as 0.000000037. What is the best way to represent this number in a user interface designed for scientists?

A cyclist travels 45 kilometers in 1.5 hours. What is the most informative way to describe the cyclist's rate of travel?

The attendance at a concert was recorded as 4,857 people. When reporting this figure in a newspaper, which rounded number would be most appropriate?

A store increased the price of a product from $25 to $30. What is the correct way to describe this change?

A map uses a scale where 1 centimeter represents 5 kilometers. If two cities are 8.5 centimeters apart on the map, what is the actual distance between them?

A microscope shows a bacterium with a size of 0.000003 meters. What is the most effective format for representing this measurement in a scientific paper?

A train covers 240 miles in 3 hours. What does the calculated rate of miles per hour indicate about the train's journey?

The estimated population of a city is 2,783,591. When presenting this number in a report, how should it be rounded for general readability?

A stock's price fell from $150 to $120. What is the most accurate way to describe this price change?

In a recipe, the ratio of water to flour is 3:5. If a baker wants to use 7.5 cups of flour, how much water is needed to maintain the recipe's proportions?

A tiny particle measures 0.0000000054 meters in diameter. How is this measurement best represented in scientific notation?

A plane flew 1,500 miles in 2.5 hours. What does calculating the rate of miles per hour reveal about this flight?

The total revenue for a small business last year was $456,789. When including this information in a business report, how should the revenue be rounded?

A product's price decreased from $40 to $34. What accurately describes the percentage change in the product's price?

A blueprint for a garden uses a scale of 1 inch equals 3 feet. If the length of the garden on the blueprint is 7.5 inches, what is the actual length of the garden?

A virus has a diameter of 0.00000012 meters. What is the most appropriate way to represent this measurement in scientific literature?

A race car travels 500 miles in 2 hours. How does expressing this as a rate of miles per hour enhance our understanding of the car's performance?

A university's endowment is valued at $1,475,389,000. How should this amount be rounded when presenting it in a university brochure?

A company's expenses decreased from $500,000 to $425,000. What is the correct way to describe this change in expenses as a percentage?

A scale model of a solar system uses a scale where 1 inch represents 25 million miles. If two planets are 4.2 inches apart on the model, what is their actual distance?

A nanoparticle has a diameter of 0.00000000055 meters. Which format most clearly represents this diameter for specialists in nanotechnology?

A satellite orbits Earth, traveling 27,000 kilometers in 6 hours. Expressing this as a rate of kilometers per hour, what does it primarily communicate about the satellite's motion?

The estimated number of stars in a galaxy is 350,000,000,000. When writing an astronomy article, how should this number be rounded to be most accessible to a general audience?

An investment portfolio grew from $75,000 to $84,000 in a year. What accurately portrays the rate of growth as a percentage?

A city planner uses a map where 1 inch equates to 0.5 miles. If a proposed railway line measures 10.4 inches on the map, what is its actual length in miles?

In an experiment, bacterial growth is observed under two conditions for 72 hours. Condition A shows consistently logarithmic growth, while Condition B initially grows slowly, followed by exponential growth, plateauing at 60 hours. What data handling approach would most effectively highlight the comparative growth patterns, including the changes in growth rate and final yield?

Company X experienced a revenue increase from $5 million to $6.5 million, while Company Y saw its revenue decrease from $8 million to $6.8 million. Which analysis appropriately contextualizes these changes by considering both absolute and percentage differences?

An architect is designing a park where a scale of 1 inch represents 10 feet. The design includes a circular fountain with an actual diameter of 35 feet and a rectangular plaza that measures 80 feet by 120 feet. What considerations must be addressed to accurately represent these features on the scale model?

A chemist measures the concentration of a solution to be 0.000000000000485 moles per liter. Which number format most clearly conveys this measurement while ensuring appropriate precision for scientific analysis?

An engineer monitors the speed of a conveyor belt, recording speeds of 2.5 meters per second, 2.8 meters per second, and 3.1 meters per second at three different times. How should these measurements be analyzed and presented to describe the rate data in a meaningful way?