Non-terminating Non-recurring Decimals MCQs Quiz | Class 9
Test your understanding of Number Systems for Class IX Mathematics (Code 041). This Unit I quiz focuses on the meaning, examples, and identification of irrational numbers, specifically non-terminating non-recurring decimals. Complete the 10 MCQs below and click Submit to check your score and download the comprehensive answer PDF.
Understanding Non-terminating Non-recurring Decimals
In the Class 9 Mathematics syllabus under Unit I: Number Systems, distinguishing between rational and irrational numbers is a core competency. While rational numbers have decimal expansions that either terminate or repeat (recur), irrational numbers possess decimal expansions that are non-terminating and non-recurring.
Key Concepts
- Terminating Decimals: The division ends after a finite number of steps (e.g., 0.5, 2.75). These are rational.
- Non-terminating Recurring Decimals: The division never ends, but a block of digits repeats infinitely (e.g., 0.333…, 1.2727…). These are also rational.
- Non-terminating Non-recurring Decimals: The division never ends, and no block of digits repeats in a pattern. These numbers are Irrational.
Examples of Irrational Numbers
The most famous examples include roots of non-perfect squares and special constants:
| Number Type | Example | Decimal Expansion (Approx.) |
|---|---|---|
| Square Roots | Square root of 2 | 1.41421356… (Never repeats) |
| Constants | Pi | 3.14159265… (Never repeats) |
| Constructed | Patterned | 0.1010010001… (Zeros increase, no period) |
Properties to Remember
- The sum or difference of a rational number and an irrational number is always irrational.
- The product or quotient of a non-zero rational number and an irrational number is always irrational.
- If you cannot write a number in the form p/q (where p and q are integers and q is not zero), it is irrational.
Extra Practice Questions
Try solving these additional problems to strengthen your grasp on the topic:
- 1. Write three different irrational numbers between the rational numbers 5/7 and 9/11.
- 2. Classify the number 0.232332333… as rational or irrational.
- 3. Is the square root of 225 rational or irrational? (Hint: check if it is a perfect square).
- 4. Explain why 3.14 is a rational number, but Pi is irrational.
- 5. Find an irrational number between 0.1 and 0.12.
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