0.2222 as a fraction
Understand the Problem
The question is asking how to express the decimal number 0.2222 as a fraction, which involves identifying the proper fraction representation for the repeating decimal.
Answer
The fraction representation of the decimal number \( 0.2222\ldots \) is \( \frac{2}{9} \).
Answer for screen readers
The fraction representation of the decimal number ( 0.2222\ldots ) is ( \frac{2}{9} ).
Steps to Solve
- Assign the Decimal to a Variable
Let ( x = 0.2222\ldots ) (where the 2 repeats indefinitely).
- Multiply to Shift the Decimal Point
Multiply both sides by 10 to move the decimal point one place to the right: $$ 10x = 2.2222\ldots $$
- Set Up a Subtraction Equation
Now, subtract the original ( x ) from this new equation: $$ 10x - x = 2.2222\ldots - 0.2222\ldots $$
- Simplify the Equation
This simplifies to: $$ 9x = 2 $$
- Solve for ( x )
Now divide both sides by 9: $$ x = \frac{2}{9} $$
The fraction representation of the decimal number ( 0.2222\ldots ) is ( \frac{2}{9} ).
More Information
The fraction ( \frac{2}{9} ) represents the repeating decimal ( 0.2222\ldots ). Repeating decimals can always be converted to fractions, and this method can be applied to any repeating decimal.
Tips
- Forgetting to account for the repeating nature of the decimal can lead to errors in solving.
- Not correctly simplifying after subtraction can yield incorrect answers.
- Misplacing the decimal during multiplication can also lead to mistakes.