MCQ
$3 . \overline{27}$ is
- Aan integer
- Ba natural number
- ✓a rational number
- Dan irrational number
✓
Answer
Correct option: C.
a rational number
(c)
$3 . \overline{27}$Let $x =3 . \overline{27}$
Then $x =3.2727$
On multiplying by 100 on both side.
$100 x =327.27$--
$\Rightarrow 100 x =324+3.272727 \ldots$
$\Rightarrow 100 x =324+ x \quad$ (from eq. (i))
$\Rightarrow 100 x - x =324$
$\Rightarrow 99 x =324$
$\Rightarrow x =\frac{324}{99}=\frac{36}{11}$
So, $3 . \overline{27}$ is a rational number.
$3 . \overline{27}$Let $x =3 . \overline{27}$
Then $x =3.2727$
On multiplying by 100 on both side.
$100 x =327.27$--
$\Rightarrow 100 x =324+3.272727 \ldots$
$\Rightarrow 100 x =324+ x \quad$ (from eq. (i))
$\Rightarrow 100 x - x =324$
$\Rightarrow 99 x =324$
$\Rightarrow x =\frac{324}{99}=\frac{36}{11}$
So, $3 . \overline{27}$ is a rational number.
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