0.14 Repeating as a Fraction
The decimal number 0.14 repeating, also known as 0.1414..., is a repeating decimal that can be converted into a fraction. In this article, we will explore how to convert 0.14 repeating into a fraction and explain the steps involved in the process.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.14 repeating, the sequence "14" repeats indefinitely, making it a repeating decimal.
Converting 0.14 Repeating into a Fraction
To convert 0.14 repeating into a fraction, we can use a simple trick. Let's start by assuming that the repeating decimal is equal to a variable, say x.
x = 0.1414...
Next, we can multiply both sides of the equation by 100 to get:
100x = 14.1414...
Now, subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 14.1414... - 0.1414...
This simplifies to:
99x = 14
Finally, we can divide both sides of the equation by 99 to solve for x:
x = 14/99
Therefore, 0.14 repeating as a fraction is equal to 14/99.
Simplifying the Fraction
The fraction 14/99 can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 7.
14 ÷ 7 = 2
99 ÷ 7 = 11
So, the simplified fraction is:
2/11
Conclusion
In conclusion, 0.14 repeating as a fraction is equal to 14/99, which can be simplified further to 2/11. This conversion process can be applied to any repeating decimal to convert it into a fraction.
