1. Find the value of 0.1 - 0. 01 + 0. 001 - 0. 0001 ?

2. How many values of k exist such that k/(2-k) is an integer ?

Solution

1) 0. 0909

Explanation: Grouping positive and negative terms as pairs and then subtracting we get (0.1 + 0. 001) - (0. 01 + 0. 0001) = 0. 1010 - 0. 0101 = 0. 0909

2) Four values.

Explanation: If k/(2-k) is always an integer, then 2-k should divide k. This is possible only if k = 0, 1, 3, 4.