# Between two rational numbers

a. there is no rational number

b. there is exactly one rational number

c. there are infinitely many rational numbers

d. there are only rational numbers and no irrational numbers

**Solution:**

A number is called a __rational number__, if it can be written in the form p/q, where p and q are integers and q ≠ 0.

Consider two rational numbers 3 and 4

Between these two rational numbers there are many rational numbers like 3.1, 3.2, 3.22, 3,223, ……

Therefore, there are infinitely many rational numbers.

**✦ Try This: **Find a rational number between 1/2 and 3/4.

Rational numbers between 1/2 and 3/4 can be written as

(1/2 + 3/4)/2

Taking __LCM__

= [(4 + 6)/8]/2

By further calculation

= (10/8)/2

Divide the numerator by 2

= 5/4 × 1/2

= 5/8

Therefore, the rational number is 5/8.

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

**NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 2**

## Between two rational numbers a. there is no rational number, b. there is exactly one rational number, c. there are infinitely many rational numbers, d. there are only rational numbers and no irrational numbers

**Summary**:

A number is called a rational number, if it can be written in the form p/q, where p and q are integers and q ≠ 0. Between two rational numbers there are infinitely many rational numbers

**☛ Related Questions:**

- Decimal representation of a rational number cannot be a. terminating, b. non-terminating, c. non-ter . . . .
- The product of any two irrational numbers is a.always an irrational number, b. always a rational num . . . .
- The decimal expansion of the number √2 is a. finite decimal, b. 1.41421, c. non-terminating recurri . . . .

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