Solve =100*[1-(1/10)^5]/1-frac{1{10}}

$$= \frac { 100 \times [ 1 - ( \frac { 1 } { 10 } ) ^ { 5 } ] } { 1 - \frac { 1 } { 10 } }$$

Evaluate

$$\frac{11111}{100}=111.11$$

Solution Steps

Calculate \frac{1}{10} to the power of 5 and get \frac{1}{100000}.

$$\frac{100\left(1-\frac{1}{100000}\right)}{1-\frac{1}{10}}$$

Convert 1 to fraction \frac{100000}{100000}.

$$\frac{100\left(\frac{100000}{100000}-\frac{1}{100000}\right)}{1-\frac{1}{10}}$$

Since \frac{100000}{100000} and \frac{1}{100000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100\times \frac{100000-1}{100000}}{1-\frac{1}{10}}$$

Subtract 1 from 100000 to get 99999.

$$\frac{100\times \frac{99999}{100000}}{1-\frac{1}{10}}$$

Express 100\times \frac{99999}{100000} as a single fraction.

$$\frac{\frac{100\times 99999}{100000}}{1-\frac{1}{10}}$$

Multiply 100 and 99999 to get 9999900.

$$\frac{\frac{9999900}{100000}}{1-\frac{1}{10}}$$

Reduce the fraction \frac{9999900}{100000} to lowest terms by extracting and canceling out 100.

$$\frac{\frac{99999}{1000}}{1-\frac{1}{10}}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{\frac{99999}{1000}}{\frac{10}{10}-\frac{1}{10}}$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{99999}{1000}}{\frac{10-1}{10}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{99999}{1000}}{\frac{9}{10}}$$

Divide \frac{99999}{1000} by \frac{9}{10} by multiplying \frac{99999}{1000} by the reciprocal of \frac{9}{10}.

$$\frac{99999}{1000}\times \frac{10}{9}$$

Multiply \frac{99999}{1000} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{99999\times 10}{1000\times 9}$$

Do the multiplications in the fraction \frac{99999\times 10}{1000\times 9}.

$$\frac{999990}{9000}$$

Reduce the fraction \frac{999990}{9000} to lowest terms by extracting and canceling out 90.

$$\frac{11111}{100}$$

Factor

$$\frac{41 \cdot 271}{2 ^ {2} \cdot 5 ^ {2}} = 111\frac{11}{100} = 111.11$$