To express the repeating decimal 3.333… as a fraction, we can follow a straightforward method.
Let’s represent the repeating decimal as x:
x = 3.333…
Next, we can multiply both sides of the equation by 10 to shift the decimal point one place to the right:
10x = 33.333…
Now, we have two equations:
1. x = 3.333…
2. 10x = 33.333…
Next, we can subtract the first equation from the second:
10x – x = 33.333… – 3.333…
9x = 30
Now, solving for x gives us:
x = 30/9
This fraction can be simplified by dividing the numerator and the denominator by 3:
x = 10/3
So, 3.333… as a fraction is 10/3.