Question

Express the following quantities as continued fractions and find the fourth convergent to each.
$\frac{1189}{3027}$

Answer 1

To Express the following quantities as continued fractions and to find the fourth convergent to each .

$\frac{1189}{3027}$

$\therefore$ the Successive quotients are $3,3,3,3,3,3,3$

and This can be written as Continued fraction

$\frac{1189}{3027}=\frac{1}{3+}\frac{1}{3+}\frac{1}{3+}\frac{1}{3+}\frac{1}{3+}\frac{1}{3+}\frac{1}{3}$

and the first four Convergents are $\frac{1}{3},\frac{3}{10},\frac{10}{33},\frac{33}{109}$

Hence , fourth Convergent is $\frac{33}{109}$ .