.24 Repeating as a Fraction
When we encounter a repeating decimal like .24, we often wonder what it represents as a fraction. In this article, we'll explore how to convert .24 repeating as 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 .24, the sequence "24" repeats indefinitely, making it a repeating decimal.
Converting .24 Repeating to a Fraction
To convert .24 repeating to a fraction, we can use the following steps:
Step 1: Let x = .24 (repeating)
Let's assign the value of .24 (repeating) to x.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 24.24 (repeating)
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 24
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
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 in this case.
x = 8/33
And there you have it! .24 repeating as a fraction is equal to 8/33.
Conclusion
Converting a repeating decimal like .24 to a fraction requires a few simple steps. By following these steps, we can easily convert any repeating decimal to a fraction. In this case, we found that .24 repeating is equal to the fraction 8/33.
