Answer:
0.333.. repeating = [tex]\frac{1}{3}[/tex]
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 [tex]\frac{p}{q}[/tex], 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
[tex]\frac{9x}{9} = \frac{3}{9}[/tex]
x = [tex]\frac{3}{9}[/tex]
When we simplify the above, we get
x = [tex]\frac{1}{3}[/tex]
So the rational number [tex]\frac{1}{3}[/tex] represents 0.333....
