Question

Express the following quantities as continued fractions and find the fourth convergent to each
$\cdot 37$

Answer 1

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

$0.37$

$=\frac{37}{100}$

$\therefore$ the Successive quotients are $2,1,2,2,1$

and This can be written as Continued fraction

$\frac{37}{100}=\frac{1}{2+}\frac{1}{1+}\frac{1}{2+}\frac{1}{2+}\frac{1}{1+}\frac{1}{3};$

Here , the fourth convergent is $\frac{7}{19}$

Hence , fourth Convergent is $\frac{7}{19}$