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Decimal Expansion of Real Numbers: Terminating and Non-Terminating Video Lecture | Crash Course: Class 9

153 videos

FAQs on Decimal Expansion of Real Numbers: Terminating and Non-Terminating Video Lecture - Crash Course: Class 9

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.
153 videos

Timeline

00:00 What is decimal form?
00:14 Types of non-terminating decimal numbers
00:15 Types of decimals
01:00 Terminating decimal numbers
01:20 Non-terminating recurring decimals
02:41 Non-terminating non-recurring decimals
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