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Rational Numbers & their Decimal Expansions Video Lecture | Crash Course: Class 10
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FAQs on Rational Numbers & their Decimal Expansions Video Lecture - Crash Course: Class 10
| 1. What are rational numbers? |  |
Ans. Rational numbers are numbers that can be expressed as a ratio or fraction of two integers, where the denominator is not zero. They include numbers such as -3/4, 2/5, and 7/2.
| 2. How are decimal expansions related to rational numbers? | |
Ans. Decimal expansions are a way to represent rational numbers in a decimal form. Rational numbers have either a finite or repeating decimal expansion. For example, 1/2 is represented as 0.5, and 1/3 is represented as 0.3333... with the 3s repeating indefinitely.
| 3. Can all rational numbers be represented as decimal expansions? | |
Ans. Yes, all rational numbers can be represented as decimal expansions. However, some rational numbers have finite decimal expansions, such as 1/4 = 0.25, while others have repeating decimal expansions, such as 1/7 = 0.142857142857...
| 4. Are there any rational numbers with non-repeating and non-terminating decimal expansions? | |
Ans. No, rational numbers always have repeating or terminating decimal expansions. This is because the decimal representation of a rational number is determined by the prime factors of its denominator. If the denominator has prime factors other than 2 and 5, the decimal expansion will repeat.
| 5. Are all decimal numbers rational? | |
Ans. No, not all decimal numbers are rational. Some decimal numbers, such as π (pi) or √2 (square root of 2), are irrational and cannot be expressed as a fraction of two integers. These numbers have non-repeating and non-terminating decimal expansions.
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Nov 24, 2024 Last updated |
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