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Chapter 1: Problem 17

A rather ordinary middle-aged man is in the hospital for a routine check-up. The nurse writes the quantity 200 on his medical chart but forgets to include the units. Which of the following quantities could the 200 plausibly represent? (a) his mass in kilograms; (b) his height in meters; (c) his height in centimeters; (d) his height in millimeters; (e) his age in months.

Short Answer

Expert verified
The quantity 200 could plausibly represent his height in centimeters.

Step by step solution

01

Analyzing Mass in Kilograms

Considering option (a), a mass of 200 kilograms is quite high for a middle-aged man, as the average mass is typically below 150 kilograms. Thus, 200 kilograms is unlikely to represent the patient's mass.
02

Evaluating Height in Meters

For option (b), a height of 200 meters would be extraordinarily tall and is clearly unreasonable for any human. Therefore, this option is not plausible.
03

Assessing Height in Centimeters

Looking at option (c), a height of 200 centimeters equates to 2 meters. While above average, it's conceivable and thus, a plausible measure of height for a particularly tall individual.
04

Considering Height in Millimeters

For option (d), a 200 millimeter height would only be 20 centimeters, which is not plausible for an adult human's height.
05

Reviewing Age in Months

Lastly, option (e) suggests an age in months. A 200-month-old individual is approximately 16.7 years old. For a middle-aged man, this is far younger than expected and thus, not plausible.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Units of Measurement
In the world of physics and daily life, understanding units of measurement is crucial. Units give meaning to numerical values, allowing us to comprehend and communicate measurements accurately. When interpreting numbers, such as the figure 200 in our exercise, the unit of measurement becomes the key to understanding the context.

Units can represent different dimensions like length, mass, or time. In the given exercise, the number 200 on a medical chart could mean different things depending on its unit:
  • Mass - Measured in kilograms or pounds, mass helps us understand the weight of objects or people.
  • Length - Expressed in meters, centimeters, millimeters, etc., to describe distances or heights.
  • Time - Typically in seconds, minutes, or months, providing insights on duration or age.
Choosing the right unit transforms an ambiguous number into a meaningful measure. This highlights the importance of always including units in calculations and records.
Problem Solving in Physics
Solving physics problems often involves translating real-world situations into mathematical models. This requires a systematic approach:
  • Identify the Known and Unknowns: Start by listing what information is given and what needs to be found.
  • Apply Relevant Principles: Use physical laws or equations related to the problem, such as Newton's laws, conservation laws, or measurement relationships.
  • Dimensional Analysis: Verify that the units align correctly throughout the calculation. This often involves converting units to a consistent system, like the SI (International System of Units).
  • Evaluate Plausibility: Check if the outcome makes sense in the real-world context.
In our exercise, recognizing the correct unit for the number 200 involved analyzing each context (e.g., human mass or height) and aligning it with realistic scenarios. By rejecting implausible ideas, like a 200-meter person, reasoning helped in pinpointing valid possibilities.
Quantitative Reasoning
Quantitative reasoning involves using numerical data to draw logical conclusions. It's a skill that combines numerical calculation with practical thinking. In the context of our exercise, it required examining possible scenarios for the number 200 on a medical chart.
  • Logical Deduction: Question each potential unit to see if it makes sense. For example, if 200 is in kilograms, consider typical human mass ranges.
  • Comparison: Compare the possibility of each unit using known standards or averages. A 200 centimeters height was considered against average human heights for plausibility.
  • Practical Application: Relate numbers to real-world benchmarks to assess their reasonable application. This ensures the conclusion is grounded in reality, like ruling out the option of a 200-month age for a middle-aged man.
Quantitative reasoning turns abstract numbers into meaningful insights. It helps ensure numerical interpretations are grounded in practical experience and acknowledged standards.

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