0.24 Repeating as a Fraction in Simplest Form
What is 0.24 Repeating?
0.24 repeating, also known as 0.242424..., is a non-terminating decimal that has a repeating pattern of 24. This type of decimal is called a repeating decimal or a recurring decimal.
Converting 0.24 Repeating to a Fraction
To convert 0.24 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.242424...
Let's assume x = 0.242424...
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 24.242424...
Step 3: Subtract the two equations
Subtract the original equation from the new equation:
100x - x = 24.242424... - 0.242424...
This simplifies to:
99x = 24
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to solve for x:
x = 24/99
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
x = 8/33
