0.02 2 Repeating as a Fraction
What is 0.02 2 Repeating?
The number 0.0222... is an example of a repeating decimal, where the digits "22" repeat indefinitely. This type of decimal is also known as a recurring decimal.
Converting 0.02 2 Repeating to a Fraction
To convert a repeating decimal to a fraction, we can use the following steps:
Step 1: Let x = 0.0222...
Let x = 0.0222... be the given repeating decimal.
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100, which is the place value of the repeating part of the decimal.
100x = 2.222...
Step 3: Subtract the original equation from the new equation
Subtract the original equation x = 0.0222... from the new equation 100x = 2.222...
99x = 2.2
Step 4: Divide both sides by 99
Divide both sides of the equation by 99.
x = 2.2/99
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 11.
x = 2/9
Therefore, the fraction equivalent of 0.0222... is 2/9.
Conclusion
In conclusion, the repeating decimal 0.0222... can be converted to a fraction by following the steps outlined above. The equivalent fraction is 2/9.
