0.02 Repeating as a Fraction
What is 0.02 Repeating?
0.02 repeating is a decimal number that has an infinite string of 02's following the decimal point. It can be written as 0.020202... where the pattern of 02 repeats indefinitely.
Converting 0.02 Repeating to a Fraction
To convert 0.02 repeating to a fraction, we can use a few different methods.
Method 1: Dividing by 99
One way to convert 0.02 repeating to a fraction is to divide by 99. This method takes advantage of the fact that 0.02 repeating is equal to 2/100, which can be rewritten as 2/(10^2).
To convert this to a fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.
2/100 = 1/50
So, 0.02 repeating as a fraction is 1/50.
Method 2: Using Algebra
Another way to convert 0.02 repeating to a fraction is to use algebra. Let's say that x = 0.020202... We can multiply both sides of the equation by 100 to get:
100x = 2.020202...
Now, we can subtract the original equation from this new equation to get:
99x = 2
Dividing both sides by 99 gives us:
x = 2/99
Simplifying this fraction, we get:
x = 1/50
Conclusion
In conclusion, 0.02 repeating as a fraction is 1/50. This can be converted using either the method of dividing by 99 or using algebra to solve for x.
