To convert the decimal 0.33333 into a fraction, we start by recognizing that this decimal is a repeating decimal, with the digit 3 repeating indefinitely.
1. **Identifying the repeating part:** The decimal can be represented as 0.3̅, where the bar indicates that the 3 continues infinitely.
2. **Setting up an equation:** We can let x equal the repeating decimal:
x = 0.33333...
3. **Multiplying to eliminate the decimal:** Next, we multiply x by 10 to shift the decimal point one place to the right:
10x = 3.33333...
4. **Subtracting the original equation from this new equation:** Now, we’ll subtract the first equation from the second:
10x - x = 3.33333... - 0.33333...
This simplifies to:
9x = 3
5. **Solving for x:** Now, divide both sides by 9:
x = 3/9
6. **Simplifying the fraction:** The fraction 3/9 can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 3:
x = 1/3
Thus, the decimal 0.33333 can be expressed as the fraction 1/3.