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Express 0.99999..... in the form {p}{q}. Are you surprised by

Question

Express $0.99999$ ..... 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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Express

0.99999

..... in the form

\frac{p}{q}

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

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Let

x = 0.99999 \dots

...(1)

Multiply eq (1) by

10

we get

10 x = 9.9999 \dots

...(2)

Substract (1) from (2), we get

\Rightarrow 9 x = 9

\Rightarrow x = \frac{1}{1} = 1

Here,

p = 1

and

q = 1

Thus,

0.9999 \dots = 1

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Question Text	Express $0.99999$ ..... in the form $\frac{p}{q}$ . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
Answer Type	Text solution:1
Upvotes	150