0.19999 Recurring as a Fraction
Have you ever wondered what 0.19999 recurring looks like as a fraction? In this article, we'll explore the conversion of this repeating decimal to a fraction.
What is 0.19999 Recurring?
0.19999 recurring is a decimal number that has a repeating pattern of 9s. It can be written as:
0.19999... (where the dots indicate that the pattern continues indefinitely)
This type of decimal is called a repeating decimal or a recurring decimal.
Converting 0.19999 Recurring to a Fraction
To convert 0.19999 recurring to a fraction, we can use a simple trick. Let's multiply the number by 100:
100 × 0.19999... = 19.999...
Now, subtract the original number from the result:
19.999... - 0.19999... = 19.8
Notice that the repeating pattern of 9s has disappeared! We're left with a simple fraction:
19/9
So, 0.19999 recurring is equal to the fraction 19/9.
Simplifying the Fraction
We can simplify the fraction further by dividing both numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 19 and 9 is 1, so the fraction remains the same:
19/9
Conclusion
In conclusion, 0.19999 recurring can be converted to a fraction by multiplying and subtracting the number, resulting in the fraction 19/9. This technique can be applied to other repeating decimals as well, making it a useful tool in mathematics.
