Question

express 0.9999 in the form of p/q where p and q are integers 8 where q is not equal to 0​

Answer 1

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Answer 2

Let us consider the rational as x

So accordingly the equation becomes :

$\longrightarrow{\tt{x = 0.99999999....}}$ - (1)

Only 9 is being repeated

So the periodicity is 1

Now we have to take a number that has one zero after the digit 1

=> It is 10

So we will multiply both the sides with 10

We get another equation :

$\longrightarrow{\tt{10x = 9.999999...}}$ -(2)

Now we will subtract (1) from (2)

$\longrightarrow{\tt{ 10x - x = 9.9999...- 0.99999....}}$

$\longrightarrow{\tt{ 9x = 9}}$

$\large{\boxed{\tt{ x = \dfrac{9}{9}}}}$