0.01 Repeating as a Fraction
What is 0.01 Repeating?
0.01 repeating, also written as 0.010101..., is a non-terminating decimal that repeats in a predictable pattern. This type of decimal is known as a repeating decimal or a recurring decimal. In this case, the repeating pattern is "01" which repeats indefinitely.
Converting 0.01 Repeating to a Fraction
To convert 0.01 repeating to a fraction, we can use a few different methods. One common method is to use the fact that the sequence of digits repeats every two digits.
Let's say we have:
x = 0.010101...
Multiply both sides by 100:
100x = 1.010101...
Now, subtract the original equation from the new equation:
99x = 1
x = 1/99
So, 0.01 repeating as a fraction is equal to:
1/99
Alternative Method
Another way to convert 0.01 repeating to a fraction is to use the formula:
a/b = (0.01)/(1 - 0.01)
where a is the numerator and b is the denominator.
In this case, we get:
a/b = (0.01)/(1 - 0.01) a/b = (0.01)/(0.99) a/b = 1/99
Again, we get the same result: 1/99.
Conclusion
In conclusion, 0.01 repeating can be converted to a fraction by using one of the methods described above. The result is a simple fraction: 1/99. This conversion is useful in many mathematical applications, such as algebra, geometry, and calculus.
