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Chapter 2: Problem 55

There are \(3 \mathrm{ft}\) in a yard. A certain piece of wood is \(3 \mathrm{ft}\) long. What is the fundamental difference between the value of \(3 f t\) in these two statements?

Short Answer

Expert verified
The fundamental difference between the value of "3 ft" in these two statements is that in the first statement, it serves as a conversion factor between feet and yards, representing the ratio of equivalency between these two units of length measurement. In the second statement, "3 ft" represents the actual length of a specific object, which is the piece of wood, providing precise information about its size.

Step by step solution

01

Understand the meaning of "3 ft" in the first statement

In the first statement, "There are 3 ft in a yard", we are given a conversion factor between two units of length, feet and yards. Here, "3 ft" represents the equivalent length in feet for 1 yard. This means that the length of 1 yard can be replaced with 3 feet in measurement.
02

Understand the meaning of "3 ft" in the second statement

In the second statement, "A certain piece of wood is 3 ft long", we are given the length of a piece of wood. Here, "3 ft" represents the actual length of an object, which is the piece of wood in this case. This means that the wood piece has a length equal to 3 feet.
03

Identify the fundamental difference between the value of "3 ft" in these two statements

In the first statement, "3 ft" serves as a conversion factor between two units of length measurement, feet and yards. It represents the ratio of equivalency between these two units. In the second statement, "3 ft" indicates the actual length of a specific object, which is the piece of wood. It provides precise information about the size of the object. The fundamental difference between the value of "3 ft" in these statements is that it acts as a conversion factor in the first statement and represents an actual length of an object in the second statement.

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