0.006 Recurring as a Fraction
In mathematics, a recurring decimal is a decimal that has a sequence of digits that repeats indefinitely. One example of a recurring decimal is 0.006, which has a repeating pattern of "006". But have you ever wondered what 0.006 recurring is as a fraction? In this article, we'll explore how to convert 0.006 recurring into a fraction.
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.1234 recurring is a recurring decimal because the sequence "1234" repeats indefinitely. Recurring decimals can be converted into fractions, and vice versa.
Converting 0.006 Recurring into a Fraction
To convert 0.006 recurring into a fraction, we can use the following steps:
Step 1: Let x = 0.006 recurring
Let's start by letting x = 0.006 recurring.
Step 2: Multiply x by 1000
Multiply x by 1000 to get:
1000x = 6.006 recurring
Step 3: Subtract x from 1000x
Subtract x from 1000x to get:
999x = 6
Step 4: Divide by 999
Divide both sides of the equation by 999 to get:
x = 6/999
Step 5: Simplify the Fraction
Simplify the fraction 6/999 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
x = 2/333
Therefore, 0.006 recurring is equal to the fraction 2/333.
Conclusion
In conclusion, 0.006 recurring can be converted into a fraction by using the steps outlined above. The resulting fraction is 2/333. This technique can be applied to convert any recurring decimal into a fraction.
