The resistance between 2 points in an electrical circuit is 1.1 Ω. What additional resistance connected across it will make the resistance exactly 1 Ω?

the new resister is 11 ohms.

Explanation:

Set it  up like this.

1/x + 1/1.1 = 1                    Subtract 1/1.1 from both sides

1/x = 1 - 1/1.1

1 - 1/1.1 = 1/11

1/x = 1/11                          Cross multiply

11 = x

If 1/11 bothers you, you could do it it another way.

1 - 1/1.1 = (1.1 - 1 ) / 1.1 = 0.1 / 1.1  Multiply top and bottom by 10

0.1*10/(1.1 * 10 ) = 1 / 11