Question

Express 0.99999........in the form of p/q are you surprised by your answers?discuss with your classmates that why the answer make the sense
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Answer 1

Answer:

Let x=0.99999⋯ ...(1)

Multiply eq (1) by 10 we get

10x=9.9999⋯ ...(2)

Substract (1) from (2), we get

⇒9x=9

⇒x=

1

1

=1

Here,

p=1 and q=1

Thus,

0.9999⋯=1

Answer 2

Answer:

Let x=0.99999⋯ ...(1)

Multiply eq (1) by 10 we get

10x=9.9999⋯ ...(2)

Substract (1) from (2), we get

⇒9x=9

⇒x=

1

1

=1

Here,

p=1 and q=1

Thus,

0.9999⋯=1