Question

Which numbers produces an irrational number when added to 5/8? A)0.777... B)-0.625 C)5/6 D)0.13241536...

Answer 1

Option D - 0.75741536

Explanation:

Given : Number
`(5)/(8)`

To find : Which numbers produces an irrational number when added to the given number?

Solution :

The given number is a rational number.

`(5)/(8)=0.625`

We know, When any irrational number is added to a rational number produces another irrational number.

So, From the given options

A) 0.777... is a rational number as it is a repeating decimal.

So, when we add it form a rational number.

`0.625+0.777..=1.402777....`

B) -0.625 is a rational number

So, when we add it form a rational number.

`0.625+(-0.625)=0`

C)
`(5)/(6)=0.83333...` is a rational number

So, when we add it form a rational number.

`0.625+0.8333=1.45833`

D) 0.13241536... is an irrational number as it is non-terminating and no9n repeating.

So, when we add it form an irrational number.

`0.625+0.13241536...=0.75741536.....`

Therefore, Option D is correct.

Answer 2

D)0.13241536...

Explanation:

An irrational number is a number which cannot be expressed as a fraction. If you add a fraction to another fraction, a new fraction is obtained, e. g., 5/8 + 5/6 = 35/24.

Options A, B can be represented as fractions (0.777... = 7/9) and (-0.625 = -625/1000); but, option D cannot.