0.1166 Repeating as a Fraction
What is 0.1166 Repeating?
0.1166 repeating is a decimal number that has a recurring pattern of 1166. This type of decimal is called a repeating decimal or a non-terminating decimal. It means that the decimal goes on indefinitely in a predictable pattern.
Converting 0.1166 Repeating to a Fraction
To convert 0.1166 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.1166...
Let's assume that x = 0.1166... (where the dots indicate that the pattern goes on indefinitely).
Step 2: Multiply Both Sides by 10000
Multiply both sides of the equation by 10000 to get rid of the decimal places:
10000x = 1166.1166...
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
9999x = 1166
Step 4: Divide Both Sides by 9999
Divide both sides of the equation by 9999 to get:
x = 1166/9999
Simplifying the Fraction
The fraction 1166/9999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is:
x = 1166/9999
So, 0.1166 repeating as a fraction is equal to 1166/9999.
Conclusion
In this article, we have successfully converted the repeating decimal 0.1166 to a fraction, which is 1166/9999. This process can be applied to any repeating decimal to convert it to a fraction.
