Solve {l}{1/2+1/20+1/200+}{+1/2000}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } + \frac { 1 } { 20 } + \frac { 1 } { 200 } + } \\ { + \frac { 1 } { 2000 } } \end{array} \right.$$

Evaluate

$$\frac{1111}{2000}=0.5555$$

Solution Steps

Least common multiple of 2 and 20 is 20. Convert \frac{1}{2} and \frac{1}{20} to fractions with denominator 20.

$$\frac{10}{20}+\frac{1}{20}+\frac{1}{200}+\frac{1}{2000}$$

Since \frac{10}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{10+1}{20}+\frac{1}{200}+\frac{1}{2000}$$

Add 10 and 1 to get 11.

$$\frac{11}{20}+\frac{1}{200}+\frac{1}{2000}$$

Least common multiple of 20 and 200 is 200. Convert \frac{11}{20} and \frac{1}{200} to fractions with denominator 200.

$$\frac{110}{200}+\frac{1}{200}+\frac{1}{2000}$$

Since \frac{110}{200} and \frac{1}{200} have the same denominator, add them by adding their numerators.

$$\frac{110+1}{200}+\frac{1}{2000}$$

Add 110 and 1 to get 111.

$$\frac{111}{200}+\frac{1}{2000}$$

Least common multiple of 200 and 2000 is 2000. Convert \frac{111}{200} and \frac{1}{2000} to fractions with denominator 2000.

$$\frac{1110}{2000}+\frac{1}{2000}$$

Since \frac{1110}{2000} and \frac{1}{2000} have the same denominator, add them by adding their numerators.

$$\frac{1110+1}{2000}$$

Add 1110 and 1 to get 1111.

$$\frac{1111}{2000}$$

Factor

$$\frac{11 \cdot 101}{2 ^ {4} \cdot 5 ^ {3}} = 0.5555$$