0.1212 Recurring as a Fraction
What is 0.1212 recurring?
0.1212 recurring is a decimal number that has a repeating pattern of digits. The pattern repeats indefinitely, making it a type of recurring decimal.
Converting 0.1212 recurring to a fraction
To convert 0.1212 recurring to a fraction, we can use a few different methods. One common method is to multiply the number by a power of 10, and then subtract the original number.
Let's start by multiplying 0.1212 recurring by 100:
100 × 0.1212 = 12.12
Now, subtract the original number from the result:
12.12 - 0.1212 = 12
This gives us an equation:
12 = 99 × 0.1212
Now, divide both sides by 99:
0.1212 = 12/99
Simplifying the fraction
We can simplify the fraction 12/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 99 is 3, so we can divide both numbers by 3:
12 ÷ 3 = 4 99 ÷ 3 = 33
This gives us the simplified fraction:
0.1212 = 4/33
Conclusion
In conclusion, 0.1212 recurring can be converted to a fraction, and the resulting fraction is 4/33. This is a simple and elegant way to express a recurring decimal as a fraction.
