0.2 Repeating 2 as a Simplified Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One example of a repeating decimal is 0.222..., where the sequence "2" repeats indefinitely. But did you know that this repeating decimal can be expressed as a simplified fraction?
Converting 0.2 Repeating 2 to a Fraction
To convert 0.2 repeating 2 to a fraction, we can use the following steps:
Let x = 0.222... (1)
Multiply both sides of the equation by 10:
10x = 2.222...
Subtract equation (1) from equation (2):
9x = 2
Divide both sides of the equation by 9:
x = 2/9
Therefore, 0.2 repeating 2 can be expressed as a simplified fraction as:
2/9
Simplifying the Fraction
To ensure that the fraction is in its simplest form, we can simplify it further by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 2 and 9 is 1, so the fraction remains:
2/9
Conclusion
In this article, we have shown that 0.2 repeating 2 can be expressed as a simplified fraction, which is 2/9. This conversion is useful in various mathematical calculations and applications, and it's always fascinating to explore the relationships between different numerical representations.
