Solve 1/99*100*101+1/100

$$\frac{ 1 }{ 99 \times 100 \times 101 } + \frac{ 1 }{ 100 }$$

Evaluate

$$\frac{100}{9999}\approx 0.010001$$

Solution Steps

Multiply 99 and 100 to get 9900.

$$\frac{1}{9900\times 101}+\frac{1}{100}$$

Multiply 9900 and 101 to get 999900.

$$\frac{1}{999900}+\frac{1}{100}$$

Least common multiple of 999900 and 100 is 999900. Convert \frac{1}{999900} and \frac{1}{100} to fractions with denominator 999900.

$$\frac{1}{999900}+\frac{9999}{999900}$$

Since \frac{1}{999900} and \frac{9999}{999900} have the same denominator, add them by adding their numerators.

$$\frac{1+9999}{999900}$$

Add 1 and 9999 to get 10000.

$$\frac{10000}{999900}$$

Reduce the fraction \frac{10000}{999900} to lowest terms by extracting and canceling out 100.

$$\frac{100}{9999}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {2} \cdot 11 \cdot 101} = 0.010001000100010001$$