What is the value of (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/100) ?

Hi - I have added few details between each step, let me know if that doesn't help.

\((1-\frac{1}{10})(1-\frac{1}{11})(1-\frac{1}{12})…(1-\frac{1}{100})\)

Step 1: For each term, multiply the numerator and denominator by the denominator of the other term so as to make the denominator common.

Ex.
\(1-\frac{1}{10} = \frac{10}{10} - \frac{1}{10} = \frac{10-1}{10}\)

\(1-\frac{1}{11} = \frac{11}{11} - \frac{1}{11} = \frac{11-1}{11}\)

so on .. to arrive at

\((\frac{10-1}{10})(\frac{11-1}{11})(\frac{12-1}{12})…(\frac{100-1}{100})\)

Step 2: Simplify the numerator

\((\frac{9}{10})(\frac{10}{11})(\frac{11}{12})…(\frac{99}{100})\)

Step 3: Observe that the numerator of each succeeding term cancels out with the denominator of its preceding term. After cancelling, the numerator of the first term term and the denominator of the last term remains as they cannot be cancelled.

\(\frac{9}{100}\)