Question

Represent the following in fractional form $(\frac{p}{q},wherep,q\in 1andq\ne 0)$
i) $1.1\overline{4}$
ii) $3.3\overline{79}$

Answer 1

(1)

Let $x=1.1\overline{4}$

$x=\mathrm{1.14444.......}$ (1)

$10x=\mathrm{11.4444.......}$ (2)

$100x=\mathrm{114.444.......}$ (3)

Subtract (2) from (3),

$100x-10x=103.0000$

$90x=103$

$x=\frac{103}{90}$$=\frac{p}{q}$

(2)

Let $x=3.3\overline{79}$

$x=\mathrm{3.3797979.......}$ (1)

$10x=\mathrm{33.7979.......}$ (2)

$1000x=\mathrm{3379.7979.......}$ (3)

Subtract (2) from (3),

$1000x-10x=3346.0000$

$990x=3346$

$x=\frac{3346}{990}$

$x=\frac{1673}{495}=\frac{p}{q}$