Converting 0.15 Repeating to a Fraction
In this article, we will explore how to convert the repeating decimal 0.15 to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.15, the sequence "15" repeats indefinitely, making it a repeating decimal.
Converting 0.15 to a Fraction
To convert 0.15 to a fraction, we can use the following steps:
Step 1: Let x = 0.15
Let's start by letting x = 0.15.
Step 2: Multiply Both Sides by 100
Multiply both sides of the equation by 100 to get:
100x = 15.15
Step 3: Subtract the Original Equation
Subtract the original equation (x = 0.15) from both sides of the new equation:
100x - x = 15.15 - 0.15
This simplifies to:
99x = 15
Step 4: Divide Both Sides by 99
Divide both sides of the equation by 99 to get:
x = 15/99
Step 5: Simplify the Fraction
The fraction 15/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3. This gives us:
x = 5/33
The Result
Therefore, the repeating decimal 0.15 is equal to the fraction 5/33.
Conclusion
Converting a repeating decimal to a fraction can be a bit challenging, but by following these steps, you can easily convert any repeating decimal to a fraction. In this case, we converted 0.15 to the fraction 5/33.
