.06 Repeating as a Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One example of a repeating decimal is 0.06. But have you ever wondered what 0.06 repeating as a fraction is? In this article, we'll explore how to convert 0.06 repeating to a fraction.
What is 0.06 Repeating?
0.06 repeating is a decimal that has a sequence of digits that repeats indefinitely. It can be written as 0.060606... where the sequence of 06 repeats forever.
Converting 0.06 Repeating to a Fraction
To convert 0.06 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.060606...
Let's start by letting x = 0.060606...
Step 2: Multiply x by 100
Next, multiply x by 100 to get:
100x = 6.060606...
Step 3: Subtract x from 100x
Now, subtract x from 100x to get:
99x = 6.000000...
Step 4: Divide by 99
Finally, divide both sides by 99 to get:
x = 6/99
Step 5: Simplify the Fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. This gives us:
x = 2/33
Therefore, 0.06 repeating as a fraction is 2/33.
Conclusion
In conclusion, 0.06 repeating as a fraction is equal to 2/33. By following the steps outlined above, you can convert any repeating decimal to a fraction. Remember to always simplify your fraction by dividing both the numerator and the denominator by their greatest common divisor to get the simplest form.
