0.15 Repeating as a Fraction in Simplest Form
Introduction
The decimal number 0.15, when it repeats indefinitely, can be converted into a fraction in its simplest form. This process involves dividing the repeating part of the decimal by a power of 10, and simplifying the resulting fraction.
Converting 0.15 Repeating to a Fraction
To convert 0.15 repeating to a fraction, we can start by writing the decimal as follows:
0.151515...
Step 1: Identify the Repeating Part
The repeating part of the decimal is "15". Let's multiply both sides of the equation by 100, which is the power of 10 that is the same length as the repeating part:
100x = 15.1515...
Step 2: Subtract the Original Equation
Now, let's subtract the original equation from the new equation:
100x - x = 15.1515 - 0.1515
This simplifies to:
99x = 14.99
Step 3: Divide by 99
Next, divide both sides of the equation by 99:
x = 14.99/99
Step 4: Simplify the Fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD):
x = 1499/9900
x = 3/20
Conclusion
Therefore, the decimal 0.15 repeating can be converted to a fraction in its simplest form as 3/20.
