Class 8 Exam > Class 8 Videos > Advance Learner Course: Mathematics (Maths) Class 8 > Decimal Expansion of Real Numbers: Terminating and Non-Terminating
Decimal Expansion of Real Numbers: Terminating and Non-Terminating Video Lecture | Advance Learner Course: Mathematics (Maths) Class 8
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FAQs on Decimal Expansion of Real Numbers: Terminating and Non-Terminating Video Lecture - Advance Learner Course: Mathematics (Maths) Class 8
| 1. What is a terminating decimal expansion? |  |
Ans. A terminating decimal expansion is a decimal number that ends after a finite number of digits. For example, the decimal expansion of 0.25 terminates because it ends at the second decimal place.
| 2. What is a non-terminating decimal expansion? | |
Ans. A non-terminating decimal expansion is a decimal number that continues indefinitely without repeating a pattern. For example, the decimal expansion of 0.333... (where the digit 3 repeats infinitely) is a non-terminating decimal.
| 3. Can all rational numbers be expressed as terminating decimal expansions? | |
Ans. Yes, all rational numbers can be expressed as terminating decimal expansions or as non-terminating repeating decimals. For example, the rational number 2/5 can be expressed as a terminating decimal 0.4, while the rational number 1/3 can be expressed as a non-terminating repeating decimal 0.333...
| 4. Are all irrational numbers non-terminating decimal expansions? | |
Ans. Yes, by definition, all irrational numbers have non-terminating decimal expansions. Irrational numbers cannot be expressed as a fraction of two integers, hence their decimal expansions continue indefinitely without repeating.
| 5. Are there any patterns in non-terminating repeating decimal expansions? | |
Ans. Yes, non-terminating repeating decimal expansions follow specific patterns. For example, the decimal expansion of 1/7 is 0.142857142857..., where the digits 142857 repeat in the same order. Such repeating patterns can be identified and used to represent the number accurately.
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Nov 15, 2024 Last updated |
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