Question

a rational number
9. If the decimal representation of a number is non-terminating, non-repeating the
(a) a natural number
(b) a rational number
(c) a whole number
(d) an irrational number
or un​

Answer 1

Answer:

decimal representation

Step-by-step explanation:

non.terminating

is irrational number

Answer 2

Answer:

(D) An irrational number

Explanation:

Rational numbers: Rational numbers refers to the numbers that can be expressed as ratio of two integers. In the form a/b where both a and b are integers and co-prime and b ≠ 0.

If we perform the division of the fraction, then we find the decimal representation is either terminating or non terminating but repeating.

ex:

(i) 2 can be expressed as 2/1, Here 2 and 1 are integers and 1 ≠ 0

(ii) 3/4, here 3 and 4 are integers and 4 ≠ 0

Irrational numbers: irrational numbers refers to the number that are not rational. i.e. cannot be expressed as a ratio of two integers. where both denominator and numerator are co-prime integers and the denominator ≠ 0. Roots of all not perfect squares are irrational.

if we express irrational numbers in decimal form, then the decimal representation is non-terminating, non-repeating

ex:

(i) π, π = 3.14159......, here decimal expansion of π is not terminating and also same pattern is not repeating.

(ii)√2, √2 = 1.14421......, here decimal expansion of √2 is not terminating and also same pattern is not repeating.

So, D is the correct option

Note:

• Real numbers are classified as rational and irrational numbers.
• Rational numbers are further divided into natural numbers, whole numbers and integers