# Decimal representation of a rational number cannot be

a. terminating

b. non-terminating

c. non-terminating repeating

d. non-terminating non-repeating

**Solution:**

We know that

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.

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__.

Decimal expansion of a rational number is either terminating or non-terminating recurring, while the decimal expansion of an irrational number is non-terminating non-recurring.

Therefore, decimal representation of a rational number cannot be __non-terminating__ non-repeating.

**✦ Try This: **Find a rational number between 2/3 and 5/6.

Rational numbers between 2/3 and 5/6 can be written as

(2/3 + 5/6)/2

Taking LCM

= [(4 + 5)/6]/2

By further calculation

= (10/6)/2

Divide the numerator by 2

= 5/3 × 1/2

= 5/6

Therefore, the rational number is 5/6.

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

**NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 3**

## Decimal representation of a rational number cannot be a. terminating, b. non-terminating, c. non-terminating repeating, d. Non-terminating non-repeating

**Summary**:

Decimal expansion of a rational number is either terminating or non-terminating recurring, while the decimal expansion of an irrational number is non-terminating non-recurring. Decimal representation of a rational number cannot be non-terminating non-repeating

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