Repeating Decimal 0.333... as a Fraction
Have you ever wondered how to convert a repeating decimal like 0.333... into a fraction? In this article, we'll explore the process of converting this repeating decimal into a simple fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.333..., the sequence of digits "3" repeats indefinitely.
Converting 0.333... into a Fraction
To convert 0.333... into a fraction, we can use the following steps:
Step 1: Let x = 0.333...
Let's start by letting x = 0.333....
Step 2: Multiply Both Sides by 10
Multiply both sides of the equation by 10, which gives us:
10x = 3.333...
Step 3: Subtract the Original Equation
Subtract the original equation from the new equation, which gives us:
10x - x = 3.333... - 0.333...
This simplifies to:
9x = 3
Step 4: Divide Both Sides by 9
Divide both sides of the equation by 9, which gives us:
x = 3/9
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3. This gives us:
x = 1/3
And that's it! We've successfully converted the repeating decimal 0.333... into a simple fraction: 1/3.
Conclusion
In conclusion, converting a repeating decimal like 0.333... into a fraction is a simple process that involves multiplying, subtracting, and dividing. By following these steps, you can convert any repeating decimal into a simple fraction.
