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Express 0.99999 .... in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense. - Mathematics

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Express 0.99999 .... in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

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Solution

Let x = 0.99999......               ........................(1)

Multiplying both sides by 10(since one digit is repeating), we get

10x = 9.9999.......              .................................(2)

(2) - (1)

⇒ 10x - x = 9

⇒ 9x = 9

⇒ x = 9/9 = 1

Thus 0.99999........................... = 1 = 1/1

Here p = 1, q = 1

Since 0.99999............goes on for ever, so there is no gap between 1 and 0.99999........ and hence they are equal 

Concept: Real Numbers and Their Decimal Expansions
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APPEARS IN

NCERT Class 9 Maths
Chapter 1 Number Systems
Exercise 1.3 | Q 4 | Page 14

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