.66 Repeating as a Fraction
What is .66 Repeating?
.66 repeating is a decimal number that has a recurring pattern of 6's after the decimal point. It is a non-terminating decimal, meaning that it cannot be expressed as a finite decimal. The pattern of 6's repeats indefinitely, making it a repeating decimal.
Converting .66 Repeating to a Fraction
To convert .66 repeating to a fraction, we can use the following steps:
Step 1: Let x = .66 Repeating
Let x = .66 repeating. This is our original decimal number.
Step 2: Multiply Both Sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 66.66 repeating
Step 3: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
99x = 66
Step 4: Divide Both Sides by 99
Divide both sides of the equation by 99 to solve for x.
x = 66/99
Step 5: Simplify the Fraction
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3.
x = 22/33
x = 2/3
Therefore, .66 Repeating as a Fraction is 2/3
The decimal .66 repeating can be expressed as a fraction, specifically 2/3. This is a simpler and more compact way of representing the decimal, and it is often used in mathematical calculations and applications.
