0.13 Repeating as a Fraction
What is 0.13 Repeating?
0.13 repeating, also known as 0.1313..., is a non-terminating and repeating decimal. This type of decimal has an infinite number of digits that follow a repeating pattern. In this case, the digits "13" are repeated indefinitely.
Converting 0.13 Repeating to a Fraction
To convert 0.13 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.13 Repeating
Let's let x equal 0.13 repeating. This means that x = 0.1313...
Step 2: Multiply x by 100
Multiply x by 100 to get rid of the decimal point. This gives us:
100x = 13.13...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 13
Step 4: Divide by 99
Divide both sides of the equation by 99 to solve for x:
x = 13/99
So, 0.13 repeating as a fraction is equal to 13/99.
Simplifying the Fraction
The fraction 13/99 is already in its simplest form, so we don't need to simplify it further.
Conclusion
In conclusion, 0.13 repeating is equal to the fraction 13/99. This conversion is useful in various mathematical applications, such as algebra, geometry, and calculus.
