Question

Express 0.3333333 …. in



form.​

Answer 1

Question :

Express 0.3333... in $\tt \frac{p}{q}$ form.

Solution :

Let x = 0.3333.. ....(1)

Then 10x = 3.3333... . ....(2)

Subtracting (1) from (2) we get

$\tt \implies$ 9x = 3

$\tt \implies$ x = $\frac{3}{9}$

$\tt \implies$ x = $\frac{1}{3}$

$\tt \therefore$ 0.333... = $\frac{1}{3}$

Answer 2

We can say that we have to prove 0.3 bar a rational So let r be the reqd. rational number. Then we can write

= 0.3333333

Since we only one digit below bar i.e. 3 lets multiply above equation by 10.Then we get

10r = 3.333333…

Now subtracting these equations we get

10r - r = 3.333333… - 0.3333333….

i.e. 9r = 3

i.e. r = 3

Hence p/q form of 0.3 bar is 3/1 i.e. 3. ❀if you like my answer thanks please❀