0.03 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 0.03 repeating into 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 0.03 repeating, the sequence of digits "03" repeats forever.
Converting 0.03 Repeating into a Fraction
To convert 0.03 repeating into a fraction, we can use the following steps:
Step 1: Let x = 0.03 repeating
Let's start by letting x equal 0.03 repeating.
Step 2: Multiply x by 100
Next, we'll multiply x by 100, which gives us:
100x = 3.03 repeating
Step 3: Subtract x from 100x
Now, we'll subtract x from 100x, which gives us:
99x = 3
Step 4: Solve for x
Finally, we'll solve for x by dividing both sides of the equation by 99:
x = 3/99
Simplifying the Fraction
We can simplify the fraction 3/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
x = 1/33
Therefore, 0.03 repeating is equal to the fraction 1/33.
Conclusion
In this article, we've learned how to convert 0.03 repeating into a fraction. By following the steps outlined above, we can convert any repeating decimal into a fraction. Remember, the key is to multiply the decimal by a power of 10 that is greater than the number of repeating digits, and then solve for x.
