0.2424 Repeating as a Fraction
The decimal 0.2424 repeating can be converted to a fraction by using a few simple steps. In this article, we will explore how to convert this repeating decimal to a 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 0.2424 repeating, the sequence "24" repeats indefinitely.
Converting 0.2424 Repeating to a Fraction
To convert 0.2424 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.2424 repeating
Let x = 0.2424 repeating. This means that x has an infinite number of 24s repeating.
Step 2: Multiply x by 100
Multiply x by 100 to get 24.24 repeating.
100x = 24.24 repeating
Step 3: Subtract x from 100x
Subtract x from 100x to get 24.
100x - x = 24 99x = 24
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get x in terms of a fraction.
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).
x = 24/99 = 8/33
Therefore, 0.2424 repeating can be written as the fraction 8/33.
Conclusion
In conclusion, we have successfully converted the repeating decimal 0.2424 to a fraction. The fraction equivalent to 0.2424 repeating is 8/33.
