To express 0.333 as a fraction, we start by recognizing that it is a repeating decimal. The repeating part is ‘3’. We can set up the equation:
x = 0.333…
Now, to eliminate the decimal, we can multiply both sides of the equation by 10:
10x = 3.333…
Next, we subtract the original equation from this new equation:
10x – x = 3.333… – 0.333…
This simplifies to:
9x = 3
Now, we solve for x:
x = 3/9
This fraction can be simplified to:
x = 1/3
Therefore, 0.333… can be expressed as the fraction 1/3.