Question

is 0.12345... a rational number or irrational number

Answer 1

Answer:

Yes it is rational number as it can be converted in fraction form 12345/100000

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Answer 2

Yes, 0.12345 is a rational number.

Given,

The number = 0.12345

To Find,

The given number is rational or irrational.

Solution,

Before solving the question, let's understand some concepts.

Rational Number:

A rational number can be written as p/q, where p and q are both integers and q is zero.

Irrational Number:

Irrational numbers cannot be expressed as p/q, where p and q are integers, and q is not equal to zero.

Terminating Decimal Expansion:

In the division process, a terminating decimal expansion occurs when the number reaches its end after a finite number of steps.

If the given number is terminating and satisfies the expression:

q is of the form $2^{n} . 5^{m}$

x = 0.12345

x = 12345/100000

x = ( 5 × 2469 )/( 5 × 20000 )

x = 2469/20000 = p/q

q = 20000 = 2⁵ × 5⁴

Therefore,

q is of the form  $2^{n} . 5^{m}$ ,

where n = 5 , m = 4

x = 0.12345 = 2469/20000

= 2469/(2⁵×5⁴)

It is a terminating decimal.

Yes, 0.12345 is a rational number.

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