0.15 Repeating as a Fraction Calculator
What is 0.15 Repeating?
0.15 repeating, also known as 0.15¯, is a decimal number that has a recurring pattern of digits. In this case, the digit 15 repeats indefinitely. This type of decimal is known as a repeating decimal or a recurring decimal.
Converting 0.15 Repeating to a Fraction
To convert 0.15 repeating to a fraction, we can use a simple trick. Let's multiply both sides of the equation by 100, which is the same as moving the decimal point two places to the right.
0.15¯ = x
Multiplying both sides by 100, we get:
15¯ = 100x
Now, subtract the original equation from the new equation:
15¯ - 0.15¯ = 100x - x
This simplifies to:
15 = 99x
Finally, divide both sides by 99:
x = 15/99
Simplifying the Fraction
We can simplify the fraction 15/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
15 ÷ 3 = 5 99 ÷ 3 = 33
So, the simplified fraction is:
5/33
Using a 0.15 Repeating as a Fraction Calculator
If you need to convert 0.15 repeating to a fraction frequently, you can use an online calculator or a converter tool. These tools can save you time and effort by providing the conversion automatically.
However, it's essential to understand the concept behind the conversion, as explained above, to appreciate the simplicity and elegance of mathematics.
Conclusion
In conclusion, 0.15 repeating can be converted to a fraction using a simple trick. The resulting fraction is 5/33, which can be simplified from the original fraction 15/99. Whether you use a calculator or do the conversion manually, understanding the process is crucial to appreciate the beauty of mathematics.
