0.13 Recurring as a Fraction
What is 0.13 Recurring?
0.13 recurring is a decimal number that has a repeating pattern of 3 after the decimal point. It is also known as a repeating decimal or a non-terminating decimal. In other words, 0.13 recurring is a decimal that goes on forever in a repeating pattern of 3, like this: 0.133333...
Converting 0.13 Recurring to a Fraction
To convert 0.13 recurring to a fraction, we can use a simple method. Let's call 0.13 recurring as x.
Step 1: Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 13.3333...
Step 2: Multiply both sides of the equation by 10 to get another equation.
10x = 1.3333...
Step 3: Subtract the two equations to eliminate the repeating decimal.
100x - 10x = 13.3333... - 1.3333...
Step 4: Simplify the equation.
90x = 12
Step 5: Divide both sides of the equation by 90 to solve for x.
x = 12/90
Simplifying the Fraction
The fraction 12/90 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 90 is 6.
12 ÷ 6 = 2 90 ÷ 6 = 15
So, the simplified fraction is:
x = 2/15
Conclusion
0.13 recurring as a fraction is equal to 2/15. This is a simple and exact conversion of the repeating decimal to a fraction.
