.2424 Repeating as a Fraction
The decimal number .2424 repeating is a non-terminating decimal that has a repeating pattern of 24. This type of decimal is also known as a repeating decimal or a non-terminating decimal. In this article, we will explore how to convert .2424 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, .12341234..., .56785678..., and .242424... are all examples of repeating decimals. These decimals have an infinite number of digits, but they follow a specific pattern that repeats over and over.
Converting .2424 Repeating to a Fraction
To convert .2424 repeating to a fraction, we can use the following steps:
Step 1: Write the decimal as a fraction with the repeating part in the numerator
Let x be the decimal .2424 repeating. Then, we can write x as a fraction with the repeating part in the numerator as follows:
x = 0.242424...
x = 24/100 + 24/10000 + 24/1000000 + ...
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 24 + 24/100 + 24/10000 + ...
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 denominator by their greatest common divisor, which is 3:
x = 8/33
Therefore, the decimal .2424 repeating is equal to the fraction 8/33.
Conclusion
In conclusion, the decimal .2424 repeating can be converted to a fraction by using the steps outlined above. The resulting fraction is 8/33, which is a simplified fraction. This conversion process can be applied to any repeating decimal to convert it into a fraction.
