Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

How do you write [tex]1.\overline{2}[/tex] as a fraction?

Sagot :

To express the repeating decimal \( 1.\overline{2} \) as a fraction, we can follow these steps:

1. Let \( x \) represent the repeating decimal:
[tex]\[ x = 1.2222\ldots \][/tex]

2. Multiply both sides of the equation by 10 to move the decimal point one place to the right:
[tex]\[ 10x = 12.2222\ldots \][/tex]

3. Subtract the original equation \( x = 1.2222\ldots \) from this new equation to eliminate the repeating part:
[tex]\[ 10x - x = 12.2222\ldots - 1.2222\ldots \][/tex]

4. Perform the subtraction:
[tex]\[ 9x = 11 \][/tex]

5. Solve for \( x \) by dividing both sides by 9:
[tex]\[ x = \frac{11}{9} \][/tex]

Therefore, \( 1.\overline{2} \) as a fraction is \(\frac{11}{9}\).

To verify, let's convert \(\frac{11}{9}\) back to a decimal:
[tex]\[ \frac{11}{9} = 1.2222\ldots \][/tex]
This confirms that our fraction [tex]\(\frac{11}{9}\)[/tex] is correct.