0.23 Repeating as a Fraction
Introduction
Repeating decimals, also known as recurring decimals, are decimal numbers that have a sequence of digits that repeat indefinitely. One such example is 0.23 repeating, a decimal that seems simple but has a more complex equivalent in fraction form.
What is 0.23 Repeating?
0.23 repeating, also written as 0.232323..., is a decimal that has a repeating pattern of 23. This pattern continues indefinitely, making it a non-terminating decimal.
Converting 0.23 Repeating to a Fraction
To convert 0.23 repeating to a fraction, we can use a simple technique. Let's assume that:
x = 0.232323...
Multiply both sides by 100 to get:
100x = 23.232323...
Now, subtract x from both sides:
100x - x = 23.232323... - 0.232323...
This simplifies to:
99x = 23
Next, divide both sides by 99:
x = 23/99
So, 0.23 repeating as a fraction is 23/99.
Simplification
We can simplify the fraction 23/99 by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 23 and 99 is 1, so the fraction remains the same:
23/99
Conclusion
In conclusion, 0.23 repeating can be converted to a fraction, which is 23/99. This fraction can be simplified, but it remains the same due to the lack of common factors between the numerator and denominator. Understanding how to convert repeating decimals to fractions is an important concept in mathematics, and this example demonstrates the simplicity and elegance of this process.
