Question

Express the following as a rational number i.e. in the form $\frac{a}{b};$ where a, $b\in I$ and $b\ne 0.$

$3.5\dot{2}$

• A. $3\frac{17}{90}$
• B. $3\frac{47}{90}$
• C. $3\frac{43}{90}$
• D. $3\frac{73}{90}$

Answer 1

The correct option is B $3\frac{47}{90}$

Let $x=\mathrm{3.5222...}$ ---- (1)
Then $10x=\mathrm{35.2222....}$ ------ (2)
Subtracting (1) from (2),
$10x-x=35.2222-3.5222$
$9x=31.7$
$x=\frac{31.7}{9}=\frac{317}{10\times 9}=3\frac{47}{90}$