Question

Which rational number equals 0 point 3 with bar over 3?

Answer 1

Answer:

0.333.. repeating = $\frac{1}{3}$

Step-by-step explanation:

The given number is 0.333...

The bar represents 3 continues forever.

Let's find the rational number that represents 0.333...

The rational number is in the form of $\frac{p}{q}$, where q ≠ 0.

Let x = 0.333...

Let's multiply both sides by 10, we get

10x = 3.33...

Now let's subtract x from 10x

10x - x  = 3.33... - 0.333..

9x = 3

Now let's divide both sides by 9, we get

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

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

When we simplify the above, we get

x  = $\frac{1}{3}$

So the rational number $\frac{1}{3}$ represents 0.333....

Answer 2

The overbar indicates the digit repeats forever. It is worth remembering that

$0.\overline{x}=\dfrac{x}{9}\qquad\text{x = any single digit}$

Your number is 3/9 = 1/3