Rational Numbers as Decimals MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz covers Unit I: Number Systems. It focuses on Rational Numbers as Decimals, specifically Terminating decimals, recurring decimals, and their conversion and identification. Answer the 10 MCQs below to test your knowledge, then submit to view your score and download the PDF answer key.
Overview: Rational Numbers and Decimal Expansions
In Class 9 Mathematics, understanding the decimal expansion of rational numbers is crucial. A rational number is any number that can be expressed in the form p/q, where p and q are integers and q is not zero. When we divide p by q, the decimal expansion behaves in one of two ways:
- Terminating Decimal: The division ends after a finite number of steps (remainder becomes zero). Examples: 1/2 = 0.5, 7/8 = 0.875.
- Non-Terminating Recurring (Repeating) Decimal: The division never ends, but a block of digits repeats periodically. Examples: 1/3 = 0.333…, 1/7 = 0.142857…
Irrational numbers, unlike rational numbers, have decimal expansions that are non-terminating and non-recurring.
Key Concepts & Rules
To identify the type of decimal expansion without performing long division, we look at the prime factorization of the denominator (q):
| Type | Condition for Denominator (q) | Example |
|---|---|---|
| Terminating | Prime factors are only 2 or 5 or both (form: 2^n * 5^m). | 3/20 (20 = 2*2*5) -> Terminating |
| Non-Terminating Recurring | Prime factors contain numbers other than 2 or 5 (e.g., 3, 7, 11). | 10/3 (3 is not 2 or 5) -> Recurring |
Conversion Techniques
From Decimal to p/q:
- Terminating: Write the digits without the decimal point as the numerator. The denominator is 1 followed by as many zeros as there are decimal places. Simplify if possible. (e.g., 0.25 = 25/100 = 1/4).
- Recurring: Let x equal the number. Multiply both sides by 10, 100, or 1000 depending on the number of repeating digits to align the decimal parts. Subtract the original equation to eliminate the recurring part. Solve for x.
Quick Revision List
- Every rational number is either a terminating or a repeating decimal.
- If the remainder becomes zero, the expansion terminates.
- If the remainder repeats, the expansion is non-terminating recurring.
- The number of digits in the repeating block is always less than the divisor.
Extra Practice Questions
- Is the decimal expansion of 129 / (2^2 * 5^7 * 7^5) terminating or non-terminating?
- Express 0.9999… in the form p/q.
- Find the length of the period of 1/11.
- Convert 3.142678 (where 2678 is not repeating, assuming standard decimal) to fraction form.
- Write the decimal expansion of 3/13 up to 4 decimal places.
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.