Solve 1-(1/10)^5/100/1-frac{1{10}}

$$\frac { 1 - ( \frac { 1 } { 10 } ) ^ { 5 } / 100 } { 1 - \frac { 1 } { 10 } }$$

Evaluate

$$\frac{1111111}{1000000}=1.111111$$

Solution Steps

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

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

Express \frac{\frac{1}{100000}}{100} as a single fraction.

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

Multiply 100000 and 100 to get 10000000.

$$\frac{1-\frac{1}{10000000}}{1-\frac{1}{10}}$$

Convert 1 to fraction \frac{10000000}{10000000}.

$$\frac{\frac{10000000}{10000000}-\frac{1}{10000000}}{1-\frac{1}{10}}$$

Since \frac{10000000}{10000000} and \frac{1}{10000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10000000-1}{10000000}}{1-\frac{1}{10}}$$

Subtract 1 from 10000000 to get 9999999.

$$\frac{\frac{9999999}{10000000}}{1-\frac{1}{10}}$$

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

$$\frac{\frac{9999999}{10000000}}{\frac{10}{10}-\frac{1}{10}}$$

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

$$\frac{\frac{9999999}{10000000}}{\frac{10-1}{10}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{9999999}{10000000}}{\frac{9}{10}}$$

Divide \frac{9999999}{10000000} by \frac{9}{10} by multiplying \frac{9999999}{10000000} by the reciprocal of \frac{9}{10}.

$$\frac{9999999}{10000000}\times \frac{10}{9}$$

Multiply \frac{9999999}{10000000} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9999999\times 10}{10000000\times 9}$$

Do the multiplications in the fraction \frac{9999999\times 10}{10000000\times 9}.

$$\frac{99999990}{90000000}$$

Reduce the fraction \frac{99999990}{90000000} to lowest terms by extracting and canceling out 90.

$$\frac{1111111}{1000000}$$

Factor

$$\frac{239 \cdot 4649}{2 ^ {6} \cdot 5 ^ {6}} = 1\frac{111111}{1000000} = 1.111111$$