Respuesta :
Answer:
Option B is correct 1/4.
Step-by-step explanation:
To find : Which number produces a rational number when added to 0.5?
Solution :
A rational number is defined as number written in simple fraction or in p/q form.
An irrational number is defined as number which cannot be written in p/q form.
We know that,
A rational number adding a rational number gives you a rational number.
A rational number adding an irrational number gives you a irrational number.
Now we take each option and check.
Option A : -1.73205081…
Number has no end and have infinite number of digits so it is irrational number.
No, this number not produce a rational number.
Option B : 1/4=0.25
Number is in form p/q so it is rational number.
Yes, this number produce a rational number.
0.25+0.5=0.75 a rational number.
Option C : 0.54732871…
Number has no end and have infinite number of digits so it is irrational number.
No, this number not produce a rational number.
Option D : [tex]\sqrt{3}[/tex]
[tex]\sqrt{3}[/tex] cannot be written in ratio so it is irrational number.
No, this number not produce a rational number.
Answer:
Option B.
Step-by-step explanation:
Rational number: If a number can be written in the form of p/q where, p and q are integers and q≠0, then the number is called a rational number.
For example: 0, 4, 1.2, 6/7 etc.
Irrational number: If a number can be written in the form of p/q where, p and q are integers and q≠0, then the number is called a rational number.
For example: √3, 4.55..., π, etc.
Using these definitions we can conclude that
0.5, 1/4 are rational numbers.
–1.73205081…, 0.54732871.., √3 are irrational numbers.
We know that sum of rational numbers is always a rational number and the sum of a rational and an irrational number is irrational.
It means only 1/4 produces a rational number when added to 0.5.
Therefore, the correct option is B.
