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 marks sense.​

Answer 1

Answer:

LET

$x = 0.9999...$

SINCE ONE DIGIT 9 IS REPEATING THEN WE WILL MULTIPLY THE ABOVE EQUATION BY 10

$= > 10x = 9.9999...$

$= > 10x = 9 + x$

$= > 10 x - x = 9$

$= > 9x = 9$

$= > x = 1$

Surprised

Answer 2

Answer:

heya mate,,

here is your answer...

Step-by-step explanation:

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

solution:

periodicity : 10[we need to multiply the power of 10 based on the no of digits repeating.here it is 10]

x=0.99999.....------------>1

10x=9.99999....---------> 2

sub 1 from 2

so,

10x=9.999..

   x= 0.999..

so the answer becomes 1

because, the .99999... part will be cancelled in the both parts

then the equation becomes..

9x=9

x=9/9

which can also be written as 1

it is surprising...

but i dont know how it can be considered valid!!!