Question

express 0.99999....... in the form p/q​

Answer 1

Answer:

Let x = 0.9999…

There is only one repeating digit so multiply by 10 we get

10x = 9.9999…

x = 0.9999…

subtract x now we get

9x = 9

Divide by 9 we get

x = 9/9 = 1

Answer 2

$\bigstar$Question:

• Expresss 0.9999.... in p/q form.

$\star$To find:

• 0.999... in p/q form.

$\star$Solution:

Let's take 0.9999.... as x.

Therefore,

x = 0.9999.....(I)

Let's multiply both the sides by 10.

Therefore,

10x = 9.9999...(II)

Now, let's subtract (I) from (II),

Therefore,

Equation(II) - Equation(I)

$\implies$10x - x = 9.99999.... - 0.9999....

$\implies$ 9x = 9

( 0.9999... and 0.9999 got cancelled)

$\implies$ x = 9/9

$\implies$ x = 1

$\star$Answer:

$\bullet$Therefore, 0.999.... in p/q form is 1