Question

Show that 0.333......is a rational number

Answer 1

Let x = 0.3333.... --------(1)
multiplying (1) with 10 we have
10x = 3.3333.... ----------(2)

Subtract eqn (2) from (1) ,
We have (2)-(1)
10x-x = 3.3333....-0.3333...
9x = 3
x = 3/9
x =1/3

We know that, by definition, rational numbers are those number which can be written in the form p/q where q not equal to zero form.

Hence 0.3333..... can be written in the form of 1/3
which implies 0.3333..... is a rational number.