0.01 Repeating as a Fraction in Simplest Form
What is 0.01 Repeating?
0.01 repeating, also known as 0.010101..., is a decimal that has a repeating pattern of 01. This decimal goes on indefinitely, with the pattern repeating every two digits. It is a non-terminating, repeating decimal.
Converting 0.01 Repeating to a Fraction
To convert 0.01 repeating to a fraction, we can use a few different methods. One way is to use the formula for converting a repeating decimal to a fraction:
x = (Decimal) / (10^n - 1)
where x is the fraction, Decimal is the repeating decimal, and n is the number of digits in the repeating pattern.
In this case, the repeating pattern has two digits (01), so we plug in the values as follows:
x = 0.010101... / (10^2 - 1) x = 0.010101... / 99
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1 and 99 is 1, so we can simplify the fraction as follows:
x = 1/99
Therefore, 0.01 repeating as a fraction in simplest form is 1/99.
Alternative Method
Another way to convert 0.01 repeating to a fraction is to use algebra. Let's say we have the equation:
x = 0.010101...
We can multiply both sides of the equation by 100 to get:
100x = 1.010101...
Subtracting x from both sides gives us:
99x = 1
Dividing both sides by 99 gives us:
x = 1/99
Again, we see that 0.01 repeating as a fraction in simplest form is 1/99.
Conclusion
In conclusion, 0.01 repeating as a fraction in simplest form is 1/99. We can convert this decimal to a fraction using either the formula or algebra, and both methods yield the same result.
