Let the rational number p / q be closest to but not equal to 22 / 7 among all rational numbers with denominator < 100 . What is the value of p-3 q ?

Step-by-step solution

We have to have | 22 7 - p q | to be as small as possible for q < 100 . | 22 7 - p q |= | 22 q-7 p 7 q | should be smallest. |22 q-7 p|=1 and q=99 aligned & p=311 & p-3 q=311-3 99=311-297=14 aligned