Solve 1/10+1/100-1/1000/10

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

Evaluate

$$\frac{109}{10000}=0.0109$$

Solution Steps

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

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

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

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

Add 10 and 1 to get 11.

$$\frac{\frac{11}{100}-\frac{1}{1000}}{10}$$

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

$$\frac{\frac{110}{1000}-\frac{1}{1000}}{10}$$

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

$$\frac{\frac{110-1}{1000}}{10}$$

Subtract 1 from 110 to get 109.

$$\frac{\frac{109}{1000}}{10}$$

Express \frac{\frac{109}{1000}}{10} as a single fraction.

$$\frac{109}{1000\times 10}$$

Multiply 1000 and 10 to get 10000.

$$\frac{109}{10000}$$

Factor

$$\frac{109}{2 ^ {4} \cdot 5 ^ {4}} = 0.0109$$