Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 55d

Chapter 1, Problem 55d

(d) Bamboo can grow up to 60.0 cm/day. Convert this growth rate into inches per hour.

Verified step by step guidance

Identify the conversion factors needed: 1 inch = 2.54 cm and 1 day = 24 hours.

Start with the given growth rate: 60.0 cm/day.

Convert centimeters to inches using the conversion factor: \( \frac{1 \text{ inch}}{2.54 \text{ cm}} \).

Convert days to hours using the conversion factor: \( \frac{1 \text{ day}}{24 \text{ hours}} \).

Combine the conversions to find the growth rate in inches per hour: \( 60.0 \text{ cm/day} \times \frac{1 \text{ inch}}{2.54 \text{ cm}} \times \frac{1 \text{ day}}{24 \text{ hours}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In this case, we need to convert centimeters to inches and days to hours. Understanding the conversion factors, such as 1 inch equals 2.54 centimeters and 1 day equals 24 hours, is essential for accurate calculations.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one unit of measurement to another by multiplying by conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is particularly useful in problems involving multiple unit conversions, as seen in this question.

Rate of Growth

The rate of growth refers to how quickly a quantity increases over time. In this context, bamboo's growth rate is given in centimeters per day, which needs to be expressed in inches per hour. Understanding how to manipulate these rates is crucial for solving problems related to growth and time.

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