0.116 Repeating as a Fraction in Simplest Form
Introduction
Repeating decimals can be a bit tricky to work with, but did you know that they can be converted into fractions? In this article, we'll explore how to convert 0.116 repeating into its simplest form as a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.116, the sequence "16" repeats indefinitely. This type of decimal is also known as a periodic decimal.
Converting 0.116 Repeating into a Fraction
To convert 0.116 repeating into a fraction, we can use a simple method. Let's start by letting x = 0.116.
Step 1: Multiply both sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 11.16
Step 2: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 11.04
Step 3: Divide both sides by 99
Divide both sides of the equation by 99 to solve for x:
x = 11.04 / 99
x = 116 / 990
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 116 and 990 is 2. Therefore, we can simplify the fraction as follows:
x = (116 ÷ 2) / (990 ÷ 2)
x = 58 / 495
Simplest Form
The simplest form of 0.116 repeating as a fraction is:
58 / 495
Conclusion
In this article, we've learned how to convert 0.116 repeating into its simplest form as a fraction. By following the steps outlined above, you can convert any repeating decimal into a fraction in its simplest form. Remember to always simplify your fractions by dividing both the numerator and the denominator by their greatest common divisor.
