.20 Repeating as a Fraction in Simplest Form
In mathematics, repeating decimals can be converted into fractions in simplest form. In this article, we will explore how to convert .20 repeating into a fraction in its simplest form.
What is .20 Repeating?
.20 repeating is a decimal that has a repeating pattern of 2 after the decimal point. It can be written as:
.202020...
Converting .20 Repeating into a Fraction
To convert .20 repeating into a fraction, we can use the following steps:
Step 1: Let x = .202020...
Let x be equal to .20 repeating.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 20.202020...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to get:
99x = 20
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 20/99
Simplify the Fraction
The fraction 20/99 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1.
x = 2/9
Therefore, .20 repeating can be written as a fraction in its simplest form as 2/9.
Conclusion
In this article, we have successfully converted .20 repeating into a fraction in its simplest form, which is 2/9. This conversion is important in mathematics as it allows us to work with fractions in various mathematical operations.
