0.144 Repeating as a Fraction
What is 0.144 Repeating?
The number 0.144 repeating, also written as 0.144444..., is a decimal that goes on forever in a repeating pattern. This type of decimal is called a repeating decimal or a non-terminating decimal. The digits 144 repeat indefinitely, making it a unique and interesting mathematical concept.
Converting 0.144 Repeating to a Fraction
To convert 0.144 repeating to a fraction, we can use a few different methods. One common approach is to use the following formula:
x = 0.144444...
100x = 14.4444...
Subtracting the original equation from the new one, we get:
99x = 14.3
x = 14.3/99
x = 43/300
So, 0.144 repeating as a fraction is 43/300.
Simplifying the Fraction
We can simplify the fraction 43/300 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 43 and 300 is 1, so the fraction is already in its simplest form:
43/300
Interesting Facts about 0.144 Repeating
- 0.144 repeating is a rational number, meaning it can be expressed as a finite decimal or a ratio of integers.
- The fraction 43/300 is an improper fraction, meaning the numerator is greater than the denominator.
- 0.144 repeating is a non-terminating, non-repeating fraction, meaning it goes on forever and never terminates, but the pattern of digits repeats indefinitely.
Conclusion
In conclusion, 0.144 repeating as a fraction is 43/300. This unique decimal has many interesting properties and can be used to explore various mathematical concepts, such as fractions, decimals, and rational numbers.
