3
$\begingroup$

What is $\left\lfloor5.\overline9\right\rfloor$ where $\lfloor.\rfloor$ denotes the floor function?

I believe it to be $6$ since converting $5.\overline9$ to fractional form yields $6$. Meanwhile my friend insists that $\left\lfloor5.\overline9\right\rfloor = 5$ since actually $5.\overline9 \ne 6$ but rather is closer to $6$ than any other real number.

Is $\left\lfloor5.\overline9\right\rfloor$ $6$ or $5$?

$\endgroup$
2
  • 8
    $\begingroup$ Welcome to Mathematics Stack Exchange. You are correct. $5.\overline9=6$ $\endgroup$
    – J. W. Tanner
    Commented Oct 12, 2020 at 14:33
  • 4
    $\begingroup$ Actually $5.\bar 9$ is exactly $6$ , not just close to $6$ , so the floor-function of $5.\bar 9$ is $6$ as well. $\endgroup$
    – Peter
    Commented Oct 12, 2020 at 14:51

1 Answer 1

Reset to default
3
$\begingroup$

You are correct.

Actually $5.\overline9=6$ (cf. this post),

so $\lfloor5.\overline9\rfloor=\lfloor6\rfloor=6$.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .