.05 Repeating as a Fraction in Simplest Form
When we are given a repeating decimal, it can be a bit challenging to convert it into a fraction. One such example is .05 repeating. In this article, we will explore how to convert .05 repeating into a fraction in its simplest form.
What is .05 Repeating?
.05 repeating is a decimal that has an infinite number of 5's after the decimal point. It can be written as:
.0505050505...
This type of decimal is known as a repeating decimal or a recurring decimal.
Converting .05 Repeating into a Fraction
To convert .05 repeating into a fraction, we can use the following steps:
Step 1: Let x be the repeating decimal .05. Then, we can write:
x = .0505050505...
Step 2: Multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 5.0505050505...
Step 3: Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 5.0505050505... - .0505050505...
This gives us:
99x = 5
Step 4: Divide both sides of the equation by 99 to solve for x:
x = 5/99
Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
x = 1/19
Therefore, .05 repeating as a fraction in simplest form is 1/19.
Conclusion
In conclusion, we have successfully converted .05 repeating into a fraction in its simplest form, which is 1/19. This process can be applied to any repeating decimal to convert it into a fraction.
