.02 Repeating as a Fraction in Simplest Form
Introduction
In mathematics, a repeating decimal is a decimal representation of a number that has an infinite sequence of repeating digits. One such repeating decimal is .02 repeating, which can be written as .020202... . But have you ever wondered what .02 repeating is equal to as a fraction in its simplest form?
Converting .02 Repeating to a Fraction
To convert .02 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:
a = d / (10^n - 1)
where:
- a is the repeating decimal
- d is the number of digits in the repeating sequence
- n is the number of digits in the repeating sequence
For .02 repeating, the repeating sequence is 02, so d = 2 and n = 2. Plugging these values into the formula, we get:
.02 = 2 / (10^2 - 1) .02 = 2 / 99 .02 = 2/99
Simplifying the Fraction
The fraction 2/99 is not in its simplest form. To simplify it, we need to find the greatest common divisor (GCD) of the numerator (2) and the denominator (99). Using the Euclidean algorithm, we find that the GCD is 1, which means the fraction is already in its simplest form.
So, the simplest form of .02 repeating as a fraction is:
.02 = 2/99
Conclusion
In conclusion, .02 repeating can be expressed as a fraction in its simplest form as 2/99. This conversion is useful in various mathematical applications, such as algebra, geometry, and calculus. Remember, converting repeating decimals to fractions can be a powerful tool in solving mathematical problems!
