Solve 1/10+1/100+1/1000+1/10000=

$$\frac { 1 } { 10 } + \frac { 1 } { 100 } + \frac { 1 } { 1000 } + \frac { 1 } { 10000 } =$$

Evaluate

$$\frac{1111}{10000}=0.1111$$

Solution Steps

Least common multiple of 10 and 100 is 100. Convert \frac{1}{10} and \frac{1}{100} to fractions with denominator 100.

$$\frac{10}{100}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}$$

Since \frac{10}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{100}+\frac{1}{1000}+\frac{1}{10000}$$

Add 10 and 1 to get 11.

$$\frac{11}{100}+\frac{1}{1000}+\frac{1}{10000}$$

Least common multiple of 100 and 1000 is 1000. Convert \frac{11}{100} and \frac{1}{1000} to fractions with denominator 1000.

$$\frac{110}{1000}+\frac{1}{1000}+\frac{1}{10000}$$

Since \frac{110}{1000} and \frac{1}{1000} have the same denominator, add them by adding their numerators.

$$\frac{110+1}{1000}+\frac{1}{10000}$$

Add 110 and 1 to get 111.

$$\frac{111}{1000}+\frac{1}{10000}$$

Least common multiple of 1000 and 10000 is 10000. Convert \frac{111}{1000} and \frac{1}{10000} to fractions with denominator 10000.

$$\frac{1110}{10000}+\frac{1}{10000}$$

Since \frac{1110}{10000} and \frac{1}{10000} have the same denominator, add them by adding their numerators.

$$\frac{1110+1}{10000}$$

Add 1110 and 1 to get 1111.

$$\frac{1111}{10000}$$

Factor

$$\frac{11 \cdot 101}{2 ^ {4} \cdot 5 ^ {4}} = 0.1111$$