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Question

Difficulty: EasyClassification of Numbers

The real number system is divided into rational and irrational numbers, with integers forming a subset of rational numbers. Which of the following numbers is classified as a rational number but is NOT an integer?

  1. 154\frac{15}{4}Answer
  2. B
    −42-42
  3. C
    25\sqrt{25}
  4. D
    π\pi

Answer

154\frac{15}{4}
The number 154\frac{15}{4} is a rational number because it is expressed as a ratio of two integers. However, since 1515 is not evenly divisible by 44, it does not simplify to a whole number, meaning it falls strictly within the rational numbers but outside the subset of integers.

Step-by-Step Solution

1
Analyze each number to determine if it is rational or irrational.
154\frac{15}{4}, −42-42, and 25\sqrt{25} can be expressed as ratios of integers, so they are rational. π\pi is known to be irrational.
The question requires finding a number that is first confirmed to be rational.
2
Identify which of the rational numbers are also integers.
−42-42 is a negative integer. 25\sqrt{25} simplifies to 55, which is a positive integer.
Integers include whole numbers and their negatives. We need to eliminate these to find a number that is not an integer.
3
Select the remaining rational number.
154\frac{15}{4} is a rational number that cannot be simplified to a whole number.
It fulfills both conditions: being a rational number and not being an integer.

Key Concept

Classification of rational numbers and integers
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Topics

Classification of Numbers

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