Real Numbers: Point-to-Number Correspondence MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz covers Unit I: Number Systems, specifically focusing on the topic of Real Numbers and the Point-to-Number Correspondence. The questions test your understanding of the principle that every real number is represented by a unique point on the number line and conversely. Complete the quiz to test your knowledge, then click Submit to review your score and download a comprehensive Answer PDF.
Understanding Real Numbers and the Number Line
In Class 9 Mathematics, Unit I: Number Systems, a fundamental concept is the relationship between real numbers and points on a geometric line. This relationship forms the basis of coordinate geometry and higher-level calculus. The set of Real Numbers (R) includes both rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or pi).
Key Concept: One-to-One Correspondence
The essence of this topic is the one-to-one correspondence between the set of real numbers and the points on a straight line. This can be summarized in two parts:
- Part 1: Every real number corresponds to a unique point on the number line. Whether the number is 5, -3.2, or an irrational number, it has a specific, distinct location.
- Part 2: Conversely, every point on the number line corresponds to a unique real number. There are no “gaps” or empty spaces on the real number line.
The Real Number Line
Because of this correspondence, the number line is often called the Real Number Line. This implies continuity. Unlike the set of integers, which has gaps between numbers (e.g., there is no integer between 1 and 2), the real number line is continuous.
Locating Irrational Numbers
While integers and fractions are easy to place, irrational numbers also have precise locations. For example, the square root of 2 can be located geometrically using the Pythagorean theorem, representing the length of the diagonal of a unit square starting from zero.
| Type of Number | Example | Position on Line |
|---|---|---|
| Integer | -2, 0, 5 | Exact markings |
| Rational | 1/2, 3.5 | Between integers |
| Irrational | Square root of 2 | Unique point (non-repeating decimal) |
Quick Revision Points
- There are infinitely many real numbers between any two given real numbers.
- The real number line is complete; no point is left without a number.
- Rational numbers alone do not fill the number line completely; irrational numbers fill the gaps.
Extra Practice Questions
- Can we represent the square root of 9.3 on the number line geometrically? (Ans: Yes)
- Is zero a rational or irrational number? (Ans: Rational)
- Find an irrational number between 1/7 and 2/7.
- True or False: Every point on the number line represents a rational number. (Ans: False, some represent irrational numbers)
- Locate square root of 3 on the number line.
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