Question

express 0.99999.... in the form p/q are you surprised by your answer ?woth your teacher and classmates discuss why the answer make sense​

Answer 1

bar is written as underline

1 (answer)

Step-by-step explanation:

Let 0.9999... = x, we say this '0.9 bar = x'.

0.9 = x ...(1)

Multiply both sides by 10 :

10 × 0.9 = 10 × x

9.9 = 10x ...(2)

Subtract (1) from (2) :

9.9 = 10x

-0.9 = - x

9 = 9x => 9 = 9x => 9/9 = x

=> 1 = x

Notice that 0.9999... is a non-terminating irrational number, but we got it equal to a number which is rational and terminating.

This is what surprises.

Answer 2

Given :-

0.99999

To Find :-

p/q form

Solution :-

Let us assume that the number is x

$\sf 0.9=x$

Multiplying both sides by 10

$\sf 0.9 \times 10 = x\times 10$

$\sf 9.9 = 10x$

So,

9.9 is almost = 10

Therefore

$\sf 10=10x$

$\sf \dfrac{10}{10} = x$

$\sf1=x$