FAQs on Rational Numbers & their Decimal Expansions

Question 1

1. What are rational numbers?

Accepted Answer

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.

Question 2

2. How are decimal expansions related to rational numbers?

Accepted Answer

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.

Question 3

3. Can all rational numbers be represented as decimal expansions?

Accepted Answer

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...

Question 4

4. Are there any rational numbers with non-repeating and non-terminating decimal expansions?

Accepted Answer

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.

Question 5

5. Are all decimal numbers rational?

Accepted Answer

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.

Rational Numbers & their Decimal Expansions Video Lecture - Crash Course

Crash Course: Class 10

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