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Fractions and Decimals — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSFractions and Decimals1 Mark
MCQ
The recurring decimal $1.\overline{263}...$ in a fraction form is equa to:
  • A
    $\frac{1262}{90}$
  • B
    ​$\frac{1262}{99}$
  • ✓
    $\frac{1262}{999}$
  • D
    $\text{None of these}$
✓

Answer

Correct option: C.
$\frac{1262}{999}$

Let $x = 1.263263263 [$we multiply it by $1000]$
Here $3$ digits are repeated
$1000x = 1263.263263.....$
$x = 1.263263....$
$999x = 1262$
$\Rightarrow\text{x}=\frac{1262}{999}$
The recurring decimal $1.263$ in a fraction form is equal to $\frac{1262}{999}.$

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