To convert the decimal 0.33333 into a rational number, we first recognize that this decimal is a repeating decimal, which can be expressed more accurately as 0.3̅ (where the line over the 3 indicates that it repeats indefinitely).
A rational number is any number that can be expressed as the fraction of two integers. In this case, we can denote:
Let x = 0.33333…
Now, to eliminate the repeating decimal, we can multiply both sides of the equation by 10:
10x = 3.33333…
Next, we can subtract the original equation from this new equation:
10x – x = 3.33333… – 0.33333…
This simplifies to:
9x = 3
Now, we can solve for x:
x = 3/9
This fraction can be simplified further:
x = 1/3
Therefore, the decimal 0.33333 (or 0.3̅) can be expressed as the rational number 1/3.