0.020 Repeating as a Fraction
In mathematics, a repeating decimal is a value that has a sequence of digits that repeats indefinitely. One such example is 0.020 repeating. In this article, we will explore how to convert 0.020 repeating into a fraction.
What is 0.020 Repeating?
0.020 repeating, also written as 0.020..., is a decimal value that has a repeating pattern of "020" indefinitely. This means that the sequence of digits "020" will continue to repeat forever.
Converting 0.020 Repeating to a Fraction
To convert 0.020 repeating to a fraction, we can use a simple method. Let's assume that the repeating decimal is equal to x:
x = 0.020...
Since the sequence "020" repeats, we can multiply both sides of the equation by 100 to get:
100x = 2.020...
Now, subtract the original equation from the new equation:
100x - x = 2.020... - 0.020...
This simplifies to:
99x = 2
Now, divide both sides by 99:
x = 2/99
The Result
Therefore, 0.020 repeating as a fraction is equal to:
2/99
This is the simplified fraction form of the repeating decimal 0.020...
