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Let’s check out your problem:

Express 0.99999 dots in the form (p)/(q). Are you surprised by your ariswer? With goof teacher and classmates discuss why the answer makes sense.

Express 0.99999… 0.99999 \ldots in the form pq \frac{p}{q} . Are you surprised by your ariswer? With goof teacher and classmates discuss why the answer makes sense.

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Full solution

Q. Express 0.99999… 0.99999 \ldots in the form pq \frac{p}{q} . Are you surprised by your ariswer? With goof teacher and classmates discuss why the answer makes sense.
  1. Define xx as 0.99999...0.99999...: Let's call 0.99999...0.99999... as xx.\newlineSo, x=0.99999...x = 0.99999...
  2. Multiply by 1010: Multiply both sides by 1010 to shift the decimal point one place to the right.\newlineSo, 10x=9.99999…10x = 9.99999\ldots
  3. Subtract to eliminate decimals: Subtract the original xx from 10x10x to get rid of the repeating decimals.\newline10x−x=9.99999...−0.99999...10x - x = 9.99999... - 0.99999...
  4. Solve for x: This gives us 9x=99x = 9.
  5. Divide by 99: Divide both sides by 99 to solve for x.\newlinex=99x = \frac{9}{9}
  6. Simplify the fraction: Simplify the fraction. x=1x = 1

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