Solve 11/10-11/100+11/1000-11/10000

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

Evaluate

$$\frac{909}{10000}=0.0909$$

Solution Steps

Multiply 1 and 10 to get 10.

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

Add 10 and 1 to get 11.

$$\frac{11}{10}-\frac{1\times 100+1}{100}+\frac{1\times 1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Multiply 1 and 100 to get 100.

$$\frac{11}{10}-\frac{100+1}{100}+\frac{1\times 1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Add 100 and 1 to get 101.

$$\frac{11}{10}-\frac{101}{100}+\frac{1\times 1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Least common multiple of 10 and 100 is 100. Convert \frac{11}{10} and \frac{101}{100} to fractions with denominator 100.

$$\frac{110}{100}-\frac{101}{100}+\frac{1\times 1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Since \frac{110}{100} and \frac{101}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{110-101}{100}+\frac{1\times 1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Subtract 101 from 110 to get 9.

$$\frac{9}{100}+\frac{1\times 1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Multiply 1 and 1000 to get 1000.

$$\frac{9}{100}+\frac{1000+1}{1000}-\frac{1\times 10000+1}{10000}$$

Add 1000 and 1 to get 1001.

$$\frac{9}{100}+\frac{1001}{1000}-\frac{1\times 10000+1}{10000}$$

Least common multiple of 100 and 1000 is 1000. Convert \frac{9}{100} and \frac{1001}{1000} to fractions with denominator 1000.

$$\frac{90}{1000}+\frac{1001}{1000}-\frac{1\times 10000+1}{10000}$$

Since \frac{90}{1000} and \frac{1001}{1000} have the same denominator, add them by adding their numerators.

$$\frac{90+1001}{1000}-\frac{1\times 10000+1}{10000}$$

Add 90 and 1001 to get 1091.

$$\frac{1091}{1000}-\frac{1\times 10000+1}{10000}$$

Multiply 1 and 10000 to get 10000.

$$\frac{1091}{1000}-\frac{10000+1}{10000}$$

Add 10000 and 1 to get 10001.

$$\frac{1091}{1000}-\frac{10001}{10000}$$

Least common multiple of 1000 and 10000 is 10000. Convert \frac{1091}{1000} and \frac{10001}{10000} to fractions with denominator 10000.

$$\frac{10910}{10000}-\frac{10001}{10000}$$

Since \frac{10910}{10000} and \frac{10001}{10000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10910-10001}{10000}$$

Subtract 10001 from 10910 to get 909.

$$\frac{909}{10000}$$

Factor

$$\frac{3 ^ {2} \cdot 101}{2 ^ {4} \cdot 5 ^ {4}} = 0.0909$$