Question

Which number produces a rational number when added to 0.5?

A. –1.73205081…
B. 1/4
C. 0.54732871…
D. √3

Answer 1

Option B.

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.

Answer 2

Option B is correct 1/4.

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 :
`√(3)`

`√(3)` cannot be written in ratio so it is irrational number.

No, this number not produce a rational number.