Solve 55/5555{frac{5/frac{frac{5{frac{8/frac{8{}}}}{}}}}{}}

$$\frac{ 55 }{ \frac{ \frac{ 5555 }{ \frac{ 5 }{ \frac{ \frac{ 5 }{ \frac{ 8 }{ \frac{ 8 }{ } } } }{ } } } }{ } }$$

Evaluate

$$\frac{1}{101}\approx 0.00990099$$

Solution Steps

Divide 55 by \frac{\frac{5555}{\frac{5}{\frac{\frac{5}{\frac{8}{\frac{8}{1}}}}{1}}}}{1} by multiplying 55 by the reciprocal of \frac{\frac{5555}{\frac{5}{\frac{\frac{5}{\frac{8}{\frac{8}{1}}}}{1}}}}{1}.

$$\frac{55}{\frac{5555}{\frac{5}{\frac{\frac{5}{\frac{8}{\frac{8}{1}}}}{1}}}}$$

Divide 5555 by \frac{5}{\frac{\frac{5}{\frac{8}{\frac{8}{1}}}}{1}} by multiplying 5555 by the reciprocal of \frac{5}{\frac{\frac{5}{\frac{8}{\frac{8}{1}}}}{1}}.

$$\frac{55}{\frac{5555\times \frac{\frac{5}{\frac{8}{\frac{8}{1}}}}{1}}{5}}$$

Divide 5 by \frac{8}{\frac{8}{1}} by multiplying 5 by the reciprocal of \frac{8}{\frac{8}{1}}.

$$\frac{55}{\frac{5555\times \frac{\frac{5\times \frac{8}{1}}{8}}{1}}{5}}$$

Anything divided by one gives itself.

$$\frac{55}{\frac{5555\times \frac{\frac{5\times 8}{8}}{1}}{5}}$$

Multiply 5 and 8 to get 40.

$$\frac{55}{\frac{5555\times \frac{\frac{40}{8}}{1}}{5}}$$

Divide 40 by 8 to get 5.

$$\frac{55}{\frac{5555\times \frac{5}{1}}{5}}$$

Anything divided by one gives itself.

$$\frac{55}{\frac{5555\times 5}{5}}$$

Multiply 5555 and 5 to get 27775.

$$\frac{55}{\frac{27775}{5}}$$

Divide 27775 by 5 to get 5555.

$$\frac{55}{5555}$$

Reduce the fraction \frac{55}{5555} to lowest terms by extracting and canceling out 55.

$$\frac{1}{101}$$

Factor

$$\frac{1}{101} = 0.009900990099009901$$