Chapter 1

NCERT
Class 9
Mathematics
Solutions
4. Express 0.999999.... in the form p/q . Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense ?

Question:

Express 0.999999.... in the form p/q . Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense ?

Answer:

Let x = 0.9999... ...(i)

Multiplying eq. (i) by 10

10x = 9.9999... ...(ii)

Subtracting eq. (i) from (ii), we get

9x = 9

x = 9/9 = 1

Hence, 0.9999... = 1

Yes, we are surprised to get an integer 1, because after decimal, 9 is repeatedly infinitely and

this will tend to an integer.

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