Question

Express the following quantities as continued fractions and find the fourth convergent to each
$1\cdot 139$

Answer 1

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

$1.139$

$=\frac{1139}{1000}$

This can be written as

$1+\frac{139}{1000}$

$\therefore$ the Successive quotients are $7,5,6,1$

and This can be written as Continued fraction

$\frac{1139}{1000}=1+\frac{1}{7+}\frac{1}{5+}\frac{1}{6+}\frac{1}{1+}\frac{1}{3};$

Here , the fourth convergent is $\frac{254}{223}$

Hence , fourth Convergent is $\frac{254}{223}$