0.3636 Repeating as a Fraction
What is 0.3636 Repeating?
0.3636 repeating is a decimal number that has a pattern of 36 repeating infinitely. This type of decimal is called a repeating decimal or a recurring decimal. It is a non-terminating decimal that has a finite number of digits that repeat in a sequence.
Converting 0.3636 Repeating to a Fraction
To convert 0.3636 repeating to a fraction, we can use a simple method. Let's assume that the repeating decimal is represented by the variable x:
x = 0.3636...
Multiply both sides by 100 to get:
100x = 36.36...
Subtract x from both sides to eliminate the repeating decimal part:
99x = 36
Now, divide both sides by 99:
x = 36/99
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 9:
x = 4/11
Therefore, 0.3636 repeating as a fraction is 4/11.
Properties of the Fraction 4/11
The fraction 4/11 is a proper fraction, where the numerator (4) is less than the denominator (11). It is also a reduced fraction, meaning that the numerator and denominator have no common factors other than 1.
Conclusion
In conclusion, 0.3636 repeating can be converted to a fraction, which is 4/11. This fraction has several interesting properties, including being a proper and reduced fraction. Understanding how to convert repeating decimals to fractions is an important concept in mathematics, and it has numerous applications in various fields, including algebra, geometry, and calculus.
