Respuesta :
Answer:
Option D - 0.75741536
Step-by-step explanation:
Given : Number [tex]\frac{5}{8}[/tex]
To find : Which numbers produces an irrational number when added to the given number?
Solution :
The given number is a rational number.
[tex]\frac{5}{8}=0.625[/tex]
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.
[tex]0.625+0.777..=1.402777....[/tex]
B) -0.625 is a rational number
So, when we add it form a rational number.
[tex]0.625+(-0.625)=0[/tex]
C) [tex]\frac{5}{6}=0.83333...[/tex] is a rational number
So, when we add it form a rational number.
[tex]0.625+0.8333=1.45833[/tex]
D) 0.13241536... is an irrational number as it is non-terminating and no9n repeating.
So, when we add it form an irrational number.
[tex]0.625+0.13241536...=0.75741536.....[/tex]
Therefore, Option D is correct.
Answer:
D)0.13241536...
Step-by-step 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.
