Solve 1/99-1/100

$$\frac { 1 } { 99 } - \frac { 1 } { 100 }$$

Evaluate

$$\frac{1}{9900}\approx 0.00010101$$

Solution Steps

Least common multiple of 99 and 100 is 9900. Convert \frac{1}{99} and \frac{1}{100} to fractions with denominator 9900.

$$\frac{100}{9900}-\frac{99}{9900}$$

Since \frac{100}{9900} and \frac{99}{9900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100-99}{9900}$$

Subtract 99 from 100 to get 1.

$$\frac{1}{9900}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2} \cdot 11} = 0.00010101010101010101$$