Solve 3+1/3+1{3+frac{1/3}}

$$3+ \frac{ 1 }{ 3+ \frac{ 1 }{ 3+ \frac{ 1 }{ 3 } } }$$

Evaluate

$$\frac{109}{33}\approx 3.303030303$$

Solution Steps

Convert 3 to fraction \frac{9}{3}.

$$3+\frac{1}{3+\frac{1}{\frac{9}{3}+\frac{1}{3}}}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{3+\frac{1}{\frac{9+1}{3}}}$$

Add 9 and 1 to get 10.

$$3+\frac{1}{3+\frac{1}{\frac{10}{3}}}$$

Divide 1 by \frac{10}{3} by multiplying 1 by the reciprocal of \frac{10}{3}.

$$3+\frac{1}{3+1\times \frac{3}{10}}$$

Multiply 1 and \frac{3}{10} to get \frac{3}{10}.

$$3+\frac{1}{3+\frac{3}{10}}$$

Convert 3 to fraction \frac{30}{10}.

$$3+\frac{1}{\frac{30}{10}+\frac{3}{10}}$$

Since \frac{30}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{\frac{30+3}{10}}$$

Add 30 and 3 to get 33.

$$3+\frac{1}{\frac{33}{10}}$$

Divide 1 by \frac{33}{10} by multiplying 1 by the reciprocal of \frac{33}{10}.

$$3+1\times \frac{10}{33}$$

Multiply 1 and \frac{10}{33} to get \frac{10}{33}.

$$3+\frac{10}{33}$$

Convert 3 to fraction \frac{99}{33}.

$$\frac{99}{33}+\frac{10}{33}$$

Since \frac{99}{33} and \frac{10}{33} have the same denominator, add them by adding their numerators.

$$\frac{99+10}{33}$$

Add 99 and 10 to get 109.

$$\frac{109}{33}$$

Factor

$$\frac{109}{3 \cdot 11} = 3\frac{10}{33} = 3.303030303030303$$