Question

4. Express 0.99999 ..., in the form p/q.Are you surprised by your answer? With your
teacher and classmates discuss why the answer makes sense​

Answer 1

Answer:

0.999... = 9/9 = 1 is the answer

Answer 2

${\sf{\huge{\underline{\red{Given :}}}}}$

Express 0.99999 .. in the form p/q.

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${\sf{\huge{\underline{\blue{Solution :}}}}}$

0.9 bar = 0.999..

Let x = 0.999..

Now,

${\sf{\green{Multiply \: both \: sides \: by \: 10 - eqn \: 1}}}$

${\sf{\green{X = 0.999}}}$

${\sf{\green{10x = 0.999 \times 10 = 9.999 - eqn \: 2}}}$

Subtract equation 1 from 2.

${\sf{\green{10x - x = 9.999-0.999}}}$

${\sf{\green{9x = 9}}}$

${\sf{\red{x = \frac{5}{5} = 1 }}}$

So,

${\sf{\blue{the \: answer \: is \: 1.}}}$

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