Question

Which number produces a rational number when added to 0.5

Answer 1

Let, the number be x

Therefore, x +0.5= p/q where q is non zero and (p, q) co-prime.

Then, x= -0.5 + (p/q)

now you can substitute any value of p and q to get x.

Answer 2

Any rational number.

Explanation:

∴
`x+0.5` is rational if and only if x is rational.

To proveL: we proceed as follows:

Suppose that
`x+0.5` is rational.

Then there are some integers p , q with
`q\\eq 0` such that

`x+(1)/(2)=(p)/(q)`

Subtract both sides by
`(1)/(2)`, we get

`x=(p)/(q)-(1)/(2)=(2p-q)/(2q)` which is rational.

Conversely, if x is rational, then there are integers a,b with b>0 such that
`x=(a)/(b)` then we have,

`x+(1)/(2)=(a)/(b)+(1)/(2)=(2a+b)/(2b)` which is also a rational.