Ex.1.3 Q4 Number System Solution - NCERT Maths Class 9

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Question

Express \(\begin{align} 0.99999…\end{align}\) in the form of \(\begin{align}\frac{p}{q}\end{align}\). Are you surprised with your Answer? With your teacher and classmates discuss why the answer makes sense?

 

 Video Solution
Number Systems
Ex 1.3 | Question 4

Text Solution

Steps:

Let  \(\begin{align}\text{ x }= 0.99999…...\qquad (1)\end{align}\)

Since one digit is repeated. We should multiply both the sides of \((1)\) by \(10\)

\[\begin{align}10\;\mathrm{x}&=9.9999 \\ 10\;\mathrm{x}&=9+0.9999 \\ 10\;\mathrm{x}&=9+\mathrm{x} \\ 10 \;\mathrm{x}-\mathrm{x}&=9 \\ 9\; \mathrm{x}&=9 \\ \mathrm{x}&=1\end{align}\]

Hence \(0.99999 = 1\)

  
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