To express the decimal 0.33333 as a fraction, we can recognize that it is a repeating decimal. The decimal 0.33333 can be rewritten as 0.3̅, where the line over the 3 indicates that it repeats indefinitely.
One common way to convert a repeating decimal to a fraction is to set it equal to a variable. Let’s denote:
x = 0.3̅
If we multiply both sides of the equation by 10, we get:
10x = 3.3̅
Now, we can subtract the original equation from this new equation:
10x – x = 3.3̅ – 0.3̅
This simplifies to:
9x = 3
Dividing both sides by 9 gives us:
x = 3/9
And we can further simplify this fraction:
x = 1/3
Therefore, the decimal 0.33333, or 0.3̅, is equal to the fraction 1/3.