0.132 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to convert 0.132 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.132 repeating, the sequence "132" repeats indefinitely.
Converting 0.132 Repeating into a Fraction
To convert 0.132 repeating into a fraction, we can use the following steps:
Step 1: Let x = 0.132...
Let's start by letting x equal 0.132 repeating.
Step 2: Multiply x by 1000
Next, let's multiply x by 1000. This will give us:
1000x = 132.132...
Step 3: Subtract x from 1000x
Now, let's subtract x from 1000x. This will give us:
999x = 132
Step 4: Divide by 999
Finally, let's divide both sides of the equation by 999. This will give us:
x = 132/999
Simplifying the Fraction
We can simplify the fraction 132/999 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 44/333
Therefore, 0.132 repeating as a fraction is equal to 44/333.
Conclusion
In this article, we've learned how to convert 0.132 repeating into a fraction. By following the steps outlined above, we can convert any repeating decimal into a fraction. Remember to always simplify your fraction by dividing both the numerator and the denominator by their greatest common divisor.
