PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
expressible in a recessing decimal.
Explanation
A rational number can be expressed as a fraction \\( \\frac{p}{q} \\). When converted to a decimal, it either terminates or repeats (recurs). Even terminating decimals can be expressed as recurring decimals by appending repeating zeros (e.g., \\( 0.5 = 0.5000... \\)). Therefore, a rational number is expressible in a recurring (written as 'recessing' in the original paper due to a typo) decimal. Irrational numbers are non-terminating and non-recurring.
Key Points
- > Rational Number Form: \\( \\frac{p}{q} \\) where \\( q \\neq 0 \\).
- > They can be terminating decimals (e.g., \\( \\frac{1}{4} = 0.25 \\)).
- > They can be non-terminating recurring decimals (e.g., \\( \\frac{2}{3} = 0.666... \\)).
- > Irrational numbers never terminate and never repeat (e.g., \\( \\sqrt{2} \\)).
- > Note: The word 'recessing' is a typographical error in the exam for 'recurring'.
- > Zero is a rational number (\\( \\frac{0}{1} \\)).
Additional Information
Types of Decimals
| Decimal Type | Example | Classification |
|---|---|---|
| Terminating | \\( 0.5 \\) | Rational |
| Non-Terminating Recurring | \\( 0.66... \\) | Rational |
| Non-Terminating Non-Recurring | \\( 1.4142... \\) | Irrational |
Memory Tips
- Rational means Predictable: If it ends or repeats, it's rational. If it's pure chaos forever (like Pi), it's irrational.