.4 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal, such as .4, into a fraction? In this article, we'll explore the steps to convert .4 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, .4 is a repeating decimal because it can be written as .444444... with the 4 repeating forever.
Converting .4 Repeating to a Fraction
To convert .4 repeating to a fraction, we can use the following steps:
Step 1: Let x = .4 Repeating
Let's start by letting x = .4 repeating. This is our repeating decimal that we want to convert to a fraction.
Step 2: Multiply Both Sides by 10
Next, we'll multiply both sides of the equation by 10. This will give us:
10x = 4.4 repeating
Step 3: Subtract x from Both Sides
Now, we'll subtract x from both sides of the equation. This will give us:
9x = 4
Step 4: Divide Both Sides by 9
Finally, we'll divide both sides of the equation by 9. This will give us:
x = 4/9
The Answer
So, the repeating decimal .4 is equal to the fraction 4/9.
Conclusion
In conclusion, converting a repeating decimal, such as .4, to a fraction is a simple process that involves multiplying, subtracting, and dividing. By following these steps, you can convert any repeating decimal to a fraction. Remember, .4 repeating is equal to 4/9!
