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

Recognize decimal as repeating: Recognize that 0.99999 is a repeating decimal, where the digit 9 repeats.Assign variable x: Let x = 0.99999.Multiply by 10: Multiply both sides of the equation by 10 to shift the decimal point one place to the right. So, 10x = 9.9999.Subtract original equation: Subtract the original equation (x = 0.99999) from the new equation (10x = 9.9999) to get 9x = 9.Divide by 9: Divide both sides by 9 to solve for x. So, x = 9/9.Simplify fraction: Simplify the fraction 9/9 to 1.Realize equivalence: Realize that 0.99999 as a fraction is 1, which is the same as 1/1.Discuss with teacher: Discuss with your teacher and classmates why this makes sense, because it seems weird but it's true that 0.99999 is just another way to write 1.

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Express $0.99999\dots$ in the form $\frac{(p)}{(q)}$ . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

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Q. Express

0.99999\dots

in the form

\frac{(p)}{(q)}

. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Recognize decimal as repeating: Recognize that $0.99999$ is a repeating decimal, where the digit $9$ repeats.
Assign variable x: Let $x = 0.99999$ .
Multiply by $10$ : Multiply both sides of the equation by $10$ to shift the decimal point one place to the right. So, $10x = 9.9999$ .
Subtract original equation: Subtract the original equation $x = 0.99999$ from the new equation $10x = 9.9999$ to get $9x = 9$ .
Divide by $9$ : Divide both sides by $9$ to solve for $x$ . So, $x = \frac{9}{9}$ .
Simplify fraction: Simplify the fraction $\frac{9}{9}$ to $1$ .
Realize equivalence: Realize that $0.99999$ as a fraction is $1$ , which is the same as $\frac{1}{1}.$
Discuss with teacher: Discuss with your teacher and classmates why this makes sense, because it seems weird but it's true that $0.99999$ is just another way to write $1$ .