Question

The number 𝒙 = 𝟏.𝟐𝟒𝟐𝟒𝟐𝟒… can be expressed in the form of 𝐱 = $\frac{p}{q}$, where 𝒑 and 𝒒 are positive integers having no common factors. Then, 𝒑 + 𝒒 equals____.

Answer 1

Option(b)
Given, x = 1.24242 .....(1)
Multiply both sides by 100,
100x = 124.2424…(2)
Subtract (1) from (2) both sides,
99x = 123,
x = $\frac{123}{99}$,

x = $\frac{41}{33}$ = $\frac{p}{q}$

Here we represent x = 1.24242… in $\frac{p}{q}$ form where,
p = 41,
q = 33,
p + q = 41 + 33 = 74.