0.1212 Repeating as a Fraction in Simplest Form
What is 0.1212 Repeating?
The decimal 0.1212 repeating is a non-terminating, recurring decimal. This means that the sequence of digits "12" repeats indefinitely. In other words, the decimal expansion of 0.1212 goes on forever in a repeating pattern.
Converting 0.1212 Repeating to a Fraction
To convert 0.1212 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.1212 Repeating
Let's assume that x = 0.1212 repeating.
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 12.1212
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 12
Step 4: Divide by 99
Divide both sides by 99 to get:
x = 12/99
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
x = 4/33
Therefore, the simplest form of 0.1212 repeating as a fraction is 4/33.
Conclusion
In conclusion, the decimal 0.1212 repeating can be expressed as a fraction in its simplest form as 4/33. This conversion is useful in various mathematical applications, such as algebra and calculus.
