Match each number on the left with the correct description of the number on the right. Answer options on the right may be used more than once.
[tex]$\pi$[/tex]
[tex]$-15$[/tex]
[tex]$-0.314314 \ldots$[/tex]
[tex]$\frac{3}{4}$[/tex]
[tex]$-0 . \overline{3}$[/tex]
This is an integer.
This is a rational number, but not an integer.
This is an irrational number.
Answer (2)
π is an irrational number.
− 15 is an integer.
− 0.314314 … is a rational number, but not an integer.
4 3 is a rational number, but not an integer.
− 0. 3 is a rational number, but not an integer.
Explanation
Problem Analysis We need to classify the given numbers into integers, rational numbers (but not integers), and irrational numbers. Let's analyze each number individually.
Classifying π The number π (pi) is a well-known irrational number. It cannot be expressed as a fraction of two integers.
Classifying -15 The number − 15 is an integer because it is a whole number with no fractional part.
Classifying -0.314314... The number − 0.314314 … is a repeating decimal, which means it can be expressed as a fraction. Therefore, it is a rational number. Since it is not a whole number, it is not an integer.
Classifying 3/4 The number 4 3 is a fraction of two integers, so it is a rational number. Since it is not a whole number, it is not an integer.
Classifying -0.3(repeating) The number − 0. 3 is a repeating decimal, specifically − 0.333 … . This can be expressed as the fraction − 3 1 , which is a rational number. Since it is not a whole number, it is not an integer.
Final Matching Matching the numbers to their descriptions:
π is an irrational number.
− 15 is an integer.
− 0.314314 … is a rational number, but not an integer.
4 3 is a rational number, but not an integer.
− 0. 3 is a rational number, but not an integer.
Examples
Understanding number classifications is crucial in many real-world applications. For instance, when calculating the circumference of a circle using C = 2 π r , the irrational nature of π means the circumference will also be irrational unless the radius is chosen carefully to cancel out the irrationality. In computer science, rational numbers are used extensively in representing precise quantities, while integers are fundamental for counting and indexing. Knowing these distinctions helps in choosing the right data types and algorithms for various tasks, from financial calculations to scientific simulations.
The number classifications are as follows: oldsymbol{\text{π}} is an irrational number, oldsymbol{-15} is an integer, and oldsymbol{-0.314314 \text{...}} , oldsymbol{\frac{3}{4}} , and oldsymbol{-0.ar{3}} are all rational numbers but not integers.
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