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There are numbers which cannot be written in the form p/q, q ≠ 0 , p, q both are integers. Is the given statement true or false? Justify

Solution:

A number which cannot be expressed in the form p/q where p and q are integers and q ≠ 0 is called an irrational number.

Also, the decimal expansion of an irrational number is neither terminating nor repeating.

Examples of irrational numbers are

1. π(pi) is an irrational number. π = 3⋅14159265… The decimal value never stops at any point.

2. √2 is an irrational number.

3. Euler's number e is an irrational number. e = 2⋅718281⋅⋅⋅⋅

4. Golden ratio, φ 1.61803398874989….

Therefore, the statement is true.

✦ Try This: State whether the following statements are true or false? Justify your answer.

When an irrational and a rational number are added, the result or their sum is an irrational number only.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.2 Problem 3(iv)

Summary:

The statement “There are numbers which cannot be written in the form p/q, q ≠ 0 , p, q both are integers” is true

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