Question

Express the following quantities as continued fractions and find the fourth convergent to each
$4\cdot 316$

Answer 1

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

$4.316$

$=\frac{4316}{1000}$

This can be written as

$4+\frac{316}{1000}$

$\therefore$ the Successive quotients are $3,6$ ;

and This can be written as Continued fraction

$4.316=4+\frac{1}{3+}\frac{1}{6+}\frac{1}{3};$

Here , the fourth Convergent is $\frac{259}{60}$

Hence , fourth Convergent is $\frac{259}{60}$